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1
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ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ู‡ุฐู‡ ู‡ูŠ ุงู„ู…ุญุงุถุฑุฉ ุงู„ุฃูˆู„ู‰
2
00:00:05,100 --> 00:00:11,520
ู„ู…ุงุฏุฉ ุฑูŠุงุถูŠุงุช ู…ู†ูุตู„ุฉ ู„ุทู„ุงุจ ูˆุทุงู„ุจุงุช ุงู„ุฌุงู…ุนุฉ
3
00:00:11,520 --> 00:00:16,680
ุงู„ุฅุณู„ุงู…ูŠุฉ ูƒู„ูŠุฉ technology ุงู„ู…ุนู„ูˆู…ุงุช ู‚ุณู… ุงู„ุญูˆุณุจุฉ
4
00:00:16,680 --> 00:00:24,200
ุงู„ู…ุชู†ู‚ู„ุฉ ุงู„ู…ุญุงุถุฑุฉ ุงู„ุฃูˆู„ู‰ ุจุนุฏ ุญุงู„ุฉ ุงู„ุทูˆุงุฑุฆ
5
00:00:26,540 --> 00:00:33,800
ุนู†ูˆุงู† ุงู„ู…ุญุงุถุฑุฉ ุงู„ู€ matrices ุฃูˆ ุงูƒู…ุงู„ ู…ุญุงุถุฑุฉ
6
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matrices ุงู„ุชูŠ ุจุฏุฃู†ุงู‡ุง ุณุงุจู‚ุงู‹ ูƒู†ุง ุนุฑูู†ุง ุดูˆ ู…ุนู†ุงุช
7
00:00:39,300 --> 00:00:46,300
matrix ูˆู‚ู„ู†ุง ุงู„ู„ูŠ ู‡ูˆ ุดูˆ ู…ุนู†ุงุช ุงู†ู‡ ุฏุฑุฌุฉ ุงู„ matrix M
8
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by N ูŠุนู†ูŠ ุนุฏุฏ ุงู„ุตููˆู M ูˆุนุฏุฏ ุงู„ุฃุนู…ุฏ Nูˆุนุฑูู†ุง ุฃูŠุถู‹ุง
9
00:00:53,050 --> 00:00:57,930
ุงู„ู„ูŠ ู‡ูˆ ุดูˆ ู…ุนู†ุงู‡ ุชุฌู…ุน two matrices ู‚ุจู„ ู‡ูŠูƒ ูˆู‚ู„ู†ุง
10
00:00:57,930 --> 00:01:02,170
ุนุดุงู† ู†ุฌู…ุน ุงู„ู„ูŠ ู‡ูˆ ู…ุตููˆูุชูŠู† ู„ุงุฒู… ูŠูƒูˆู† ุงู„ู…ุตููˆูุชูŠู†
11
00:01:02,170 --> 00:01:06,050
ู†ูุณ ุงู„ุฏุฑุฌุฉ ูŠุนู†ูŠ ู„ูˆ ูƒุงู†ุช ุงู„ู…ุตููˆูุฉ ุงู„ุฃูˆู„ู‰ ุชู„ุงุชุฉ ููŠ
12
00:01:06,050 --> 00:01:09,820
ุชู„ุงุชุฉ ุจุฏู‡ุง ุชูƒูˆู† ุงู„ู…ุตููˆูุฉ ุงู„ุชุงู†ูŠุฉ ุงู„ู„ูŠ ุจู†ุฌู…ุนู‡ุงู‡ูŠู‡ุง
13
00:01:09,820 --> 00:01:12,740
ุฃูŠุถุง ุชู„ุงุชุฉ ููŠ ุชู„ุงุชุฉ ูˆุนู…ู„ูŠุฉ ุงู„ุฌู…ุน ุฒูŠ ู…ุง ุงู†ุชูˆุง
14
00:01:12,740 --> 00:01:17,740
ุนุงุฑููŠู† ูƒู„ entry ู…ุน ุงู„ entry ุงู„ู…ู‚ุงุจู„ ู„ู‡ู… ุจุนุฏ ู‡ูŠูƒ
15
00:01:17,740 --> 00:01:21,980
ุนุฑูู†ุง ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุงู„ู„ูŠ ู‡ูˆ two matrices ูˆู‚ู„ู†ุง ุนุดุงู†
16
00:01:21,980 --> 00:01:27,380
ู†ุถุฑุจ ุงู„ matrix ุงู„ู„ูŠ ุฏุฑุฌุชู‡m by k ู„ุงุฒู… ุงู„ู„ูŠ ู‡ูˆ ูŠูƒูˆู†
17
00:01:27,380 --> 00:01:31,660
ุงู„ matrix ุงู„ุชุงู†ูŠ k by something ูŠุนู†ูŠ k by n ูŠุนู†ูŠ
18
00:01:31,660 --> 00:01:35,780
ุนุฏุฏ ุงู„ู„ูŠ ู‡ูˆ ุงู„ุฃุนู…ุฏุฉ ููŠ ุงู„ matrix ุงู„ุฃูˆู„ ูŠุณุงูˆูŠ ุนุฏุฏ
19
00:01:35,780 --> 00:01:39,640
ุงู„ุตููˆู ููŠ ุงู„ matrix ุงู„ุชุงู†ูŠ ุนุณุงุณ ุงู„ู„ูŠ ู‡ูˆ ุงู„ู„ูŠ ู‡ูˆ
20
00:01:39,640 --> 00:01:44,640
ุชูƒูˆู† ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุจูŠู† a ูˆb ุนู…ู„ูŠุฉ ู…ุนุฑูุฉูˆ ู‚ูˆู„ู†ุง ูƒูŠู
21
00:01:44,640 --> 00:01:48,560
ุงู„ู„ูŠ ู‡ูŠ ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุงู„ู„ูŠ ู‡ูˆ ู…ุตููˆูุชูŠู† ู…ุน ุจุนุถ ูˆ
22
00:01:48,560 --> 00:01:52,380
ู‚ูˆู„ู†ุง ุนุดุงู† ู†ุถุฑุจ ู…ุตููˆูุชูŠู† ู‡ูŠ ุงู„ู…ุตููˆูุฉ ู‡ุฐู‡ ู…ุซู„ุง ู…ู†
23
00:01:52,380 --> 00:01:56,020
ุงู„ุฏุฑุฌุฉ ุงู„ู„ูŠ ู‡ูˆ ู‡ุงูŠ ุตู ุตููŠู† ุชู„ุงุชุฉ ุฃุฑุจุนุฉ ู…ู† ุงู„ุฏุฑุฌุฉ
24
00:01:56,020 --> 00:02:01,560
ุฃุฑุจุนุฉ ููŠ ุชู„ุงุชุฉ ูŠุนู†ูŠ ุฃุฑุจุน ู…ุตููˆู .. ุฃุฑุจุน ุตููˆู ูˆ ุชู„ุงุช
25
00:02:01,560 --> 00:02:07,020
ุฃุนู…ุฏุฉุจู†ุถุฑุจู‡ุง ููŠ ู…ุตููˆูุฉ ุชุงู†ูŠุฉ ุชู„ุช ุตููˆู ูˆ ุนู…ูˆุฏูŠู†
26
00:02:07,020 --> 00:02:10,960
ู…ุนู†ุงุชู‡ ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุฌุงุฆุฒุฉ ูˆ ุจูŠุตูŠุฑ ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ู…ูŠุฌ
27
00:02:10,960 --> 00:02:15,000
ุจู†ุถุฑุจ ุงู„ุตู ุงู„ู„ูŠ ู‡ูˆ ุงู„ุฃูˆู„ ููŠ ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ ุจู†ุถุฑุจ
28
00:02:15,000 --> 00:02:19,240
ูˆุงุญุฏ ููŠ ุงุชู†ูŠู† ุฒุงุฆุฏ ุณูุฑ ููŠ ูˆุงุญุฏ ุฒุงุฆุฏ ุฃุฑุจุนุฉ ููŠ ุชู„ุงุชุฉ
29
00:02:19,240 --> 00:02:23,380
ูˆ ุงู„ู„ูŠ ุจูŠุทู„ุน ุนู†ุฏู‰ ุจูŠูƒูˆู† ู‡ูˆ ุงู„ entry ุงู„ุฃูˆู„ ุนู†ุฏ ุงู„
30
00:02:23,380 --> 00:02:28,440
seminar c11 ุจู†ูุณ ุงู„ุฃุณู„ูˆุจ ุงู„ู„ูŠ ู‡ูˆ ุจู†ุงุฎุฏ ุงู„ู„ูŠ ู‡ูˆ
31
00:02:28,440 --> 00:02:33,350
ุงู„ุตู ุงู„ุฃูˆู„ ููŠ ุงู„ุนู…ูˆุฏ ุงู„ุซุงู†ูŠ ุจู†ุญุตู„ ุนู„ู‰ ุงู„ุนู†ุตุฑC12
32
00:02:33,350 --> 00:02:39,390
ูˆุฎู„ุตู†ุง ู…ู† ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ุจู†ุฌูŠ ู„ู„ุณุทุฑ ุงู„ุซุงู†ูŠ ููŠ ุงู„ุนู…ูˆุฏ
33
00:02:39,390 --> 00:02:44,130
ุงู„ุฃูˆู„ ุจู†ุฌูŠุจ ุฃูˆู„ ูˆุงุญุฏ ููŠ ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ููŠ ุญุตู„ ู†ุชุฌ
34
00:02:44,130 --> 00:02:49,450
ุงู„ุถุฑุจ ูˆู‡ูƒุฐุง ู„ู…ุง ู†ูƒู…ู„ ุงู„ู„ูŠ ู‡ูˆ ุงู„ู…ุตููˆูุฉ ูƒุงู…ู„ ุงู„ู„ูŠ ู‡ูŠ
35
00:02:49,450 --> 00:02:54,990
ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ูƒู…ุง ุดุฑุญู†ุงู‡ุง ุณุงุจู‚ุง ู…ุงููŠุด ุฏุงุนูŠ ุฃู†ู†ุง
36
00:02:54,990 --> 00:03:00,450
ู†ุนูŠุฏู‡ุงูˆุงุฎุฏู†ุง ุฃู…ุซู„ุฉ ุนู„ู‰ ุถุฑุจ ู…ุตู‡ูˆูุงุช ูˆู‚ู„ู†ุง ุงู„ู…ุตู‡ูˆูุฉ
37
00:03:00,450 --> 00:03:04,590
A B ู„ูŠุณ ุดุฑุทุง ุฃู†ู‡ุง ุชุณุงูˆูŠ ุงู„ู…ุตู‡ูˆูุฉ B A ูˆู‡ูŠุนู†ู‰ ู…ุซุงู„
38
00:03:04,590 --> 00:03:09,230
ุนู„ู‰ ุฐู„ูƒ ุจุนุฏูŠู† ุนุฑูู†ุง ุดูˆ ู…ุนู†ุงุช ู…ุตู‡ูˆูุฉ ุงู„ูˆุญุฏุฉ ู…ุตู‡ูˆูุฉ
39
00:03:09,230 --> 00:03:12,110
ุงู„ูˆุญุฏุฉ ุงู„ู„ู‰ ุจูŠูƒูˆู† ุนู†ุงุตุฑ ุงู„ู‚ุทุฑ ุงู„ุฑุฆูŠุณู‰ ูˆุงุญุฏ ูˆุงุญุฏ
40
00:03:12,110 --> 00:03:15,650
ูˆุงู„ุจุงู‚ู‰ ุนู†ุงุตุฑ ุงู„ุตูุงุฑ ุณูˆุงุก ู…ุตู‡ูˆูุฉ ุงู„ูˆุญุฏุฉ ู…ู† ุฏุฑุฌุฉ
41
00:03:15,650 --> 00:03:18,970
ุงุชู†ูŠู† ููŠ ุงุชู†ูŠู† ุงูˆ ู…ุตู‡ูˆูุฉ ุงู„ูˆุญุฏุฉ ู…ู† ุฏุฑุฌุฉ ุชู„ุงุชุฉ ููŠ
42
00:03:18,970 --> 00:03:24,570
ุชู„ุงุชุฉ ุจู†ูุณ ุงู„ุงุณู„ูˆุจุนุฑูู†ุง ุงู„ู„ูŠ ู‡ูˆ ู…ุฏูˆุฑ ุงู„ู…ุตููˆูุฉ ุฃูˆ A
43
00:03:24,570 --> 00:03:29,230
Transverse ุงู„ู„ูŠ ู‡ูŠ ุนู…ู„ูŠุฉ ุชุญูˆูŠู„ ุงู„ุตููˆู ุฅู„ู‰ ุฃุนู…ุฏุฉ ูˆ
44
00:03:29,230 --> 00:03:36,390
ู‚ู„ู†ุง ูƒูŠู ุจู†ุญูˆู„ู‡ุง ุณุงุจู‚ุง ู‚ู„ู†ุง ุนู…ู„ูŠุฉ ุถุฑุจ A R ุงู„ู…ุชูƒุฑุฑุฉ
45
00:03:36,390 --> 00:03:40,890
A R ู…ุนู†ุงุชู‡ ุฃู†ู‡ ุถุฑุจู†ุง ุงู„ matrix ููŠ ู†ูุณู‡ R ู…ู† ุงู„ู…ุฑุงุช
46
00:03:40,890 --> 00:03:44,810
ู„ู…ุง ู†ู‚ูˆู„ A ุฃูˆ ุงู„ุณูุฑ ู†ุนู†ูŠ ุงู„ุจู‚ูŠุฉ ุงู„ู„ูŠ ู‡ูˆ ุงู„ู…ุตูˆูุฉ
47
00:03:44,810 --> 00:03:50,320
ุงู„ู…ุตูˆูุฉ ุงู„ูˆุญุฏุฉุงู„ู„ูŠ ู‡ูŠ ู…ู† ุงู„ุฏุฑุฌุฉ ุงู„ู„ูŠ ู‡ูŠ ุงู„ู†ูŠุฉ ุญุณุจ
48
00:03:50,320 --> 00:03:54,980
ุงู„ู„ูŠ ู‡ูŠ ุงู„ู€ A ุงู„ู„ูŠ ุจู†ุญูƒูŠ ุนู†ู‡ุง ุนุฑูู†ุง ุดูˆ ู…ุนู†ุงุชู‡ ุงู„ู„ูŠ
49
00:03:54,980 --> 00:04:02,000
ู‡ูˆ ุงู„ matrix ูŠูƒูˆู† symmetric ูˆ ุจุนุฏูŠู† ุฃุฌูŠู†ุง ุงู„ู„ูŠ ู‡ูˆ
50
00:04:02,000 --> 00:04:06,220
ุฃูˆุตู„ู†ุง ู„ู„ู…ูˆุถูˆุน ุงู„ู„ูŠ ุงุญู†ุง ุงู„ูŠูˆู… ุจุฏู†ุง ู†ูุตู„ ููŠู‡ ูˆ
51
00:04:06,220 --> 00:04:10,400
ุญูƒูŠู†ุง ุจุฑุถู‡ ู…ู‚ุฏู…ุฉ ููŠู‡ ููŠ ุงู„ู…ุญุงุถุฑุฉ ู‚ู„ู†ุง ุงู„ู„ูŠ ู‡ูˆ ุญุงุฌุฉ
52
00:04:10,400 --> 00:04:15,040
ุงุณู…ู‡ุง zero one matrix ู‡ุฐู‡ ุนุจุงุฑุฉ ุนู† ู…ุตููˆูุฉูƒู„
53
00:04:15,040 --> 00:04:19,640
ุนู†ุงุตุฑู‡ุง ุนุจุงุฑุฉ ุนู† ูŠุง ุณูุฑ ูŠุง ูˆุงุญุฏ ุนู†ุงุตุฑ ุงู„ู…ุตููˆูุฉ ูŠุง
54
00:04:19,640 --> 00:04:23,920
ุณูุฑ ูŠุง ูˆุงุญุฏ ููŠ ุนู†ุฏู†ุง ุนู…ู„ูŠุฉ ุจุฏู†ุง ู†ุฌุฑูŠู‡ุง ุจูŠู†
55
00:04:23,920 --> 00:04:27,780
ุงู„ู…ุตููˆูุงุช ุงุณู…ู‡ุง ุงู„ู€ Boolean Operations ุงู„ู€ Boolean
56
00:04:27,780 --> 00:04:33,220
Operations ุจูŠู† ุงู„ู„ูŠ ู‡ูŠ ุงู„ู…ุตููˆูุชูŠู† ู‡ู†ุนุฑูู‡ุง ุจุนุฏ ุดูˆูŠุฉ
57
00:04:33,220 --> 00:04:39,570
ุงู„ู„ูŠ ู‡ูŠ ุงูˆ ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุงู„ุจูˆู„ูŠู†ูŠุฃูˆู„ ุงุดูŠ ุจุฏู†ุง ู†ุนุฑู
58
00:04:39,570 --> 00:04:44,010
ุดูˆ ู…ุนู†ุงุช ุงู„ู€ Boolean operation ุจูŠู† ุงู„ุตูุฑ ูˆุงู„ูˆุงุญุฏ
59
00:04:44,010 --> 00:04:48,510
ุงู„ู„ูŠ ู‡ู…ุง ุนู†ุงุตุฑ ุงู„ู€ 01 matrix ุงู„ู„ูŠ ุงุญู†ุง ุจุฏู†ุง ู†ุฌุฑูŠ
60
00:04:48,510 --> 00:04:53,870
ุนู„ูŠู‡ ุนู…ู„ูŠุฉ ุงู„ู€ Boolean operation ูˆุจุฑุถู‡ ุฐูƒุฑู†ุงู‡ุง ููŠ
61
00:04:53,870 --> 00:04:59,570
ุงู„ู…ุญุงุถุฑุฉ ู‚ู„ู†ุง ุนุดุงู† ุจุฏู†ุง ู†ุนุฑู ุดูˆ ู…ุนู†ุงุช ุนู…ู„ูŠุชูŠู† ุงู„ู€
62
00:04:59,570 --> 00:05:02,970
Boolean operations ุนู†ุฏู†ุง ุงู„ู„ูŠ ู‡ูŠ ุงู„ meet ูˆุงู„ joint
63
00:05:03,390 --> 00:05:06,670
ูˆู‚ู„ู†ุง ู†ุชุฎูŠู„ ุงู„ meet ูˆ ุงู„ join ุทุจุนุง ุงู„ b1 ูˆ ุงู„ b2
64
00:05:06,670 --> 00:05:10,850
ู‡ุฏูˆู„ ุงู„ู„ูŠ ุจู†ุนู…ู„ู‡ู… meet ุงูˆ ู†ุนู…ู„ู‡ู… joint ู‡ุฏูˆู„ ุงู„ b1
65
00:05:10,850 --> 00:05:15,610
ูˆ ุงู„ b2 ูŠุง ุจูŠุงุฎุฏู† 0 ูŠุง ุจูŠุงุฎุฏู† ุงูŠุงุด 1 ูุงู„ุงู† ุนู…ู„ูŠุฉ
66
00:05:15,610 --> 00:05:22,070
ุงู„ meet ุงู„ู„ูŠ ู‡ูŠ ุจุชุฐูƒุฑู†ุง ูˆ ูƒุฃู†ู‡ ุงุญู†ุง ู‚ู„ู†ุง ุงู†ู‡ ุจู†ุฐูƒุฑ
67
00:05:22,070 --> 00:05:26,890
ุงู„ู„ูŠ ู‡ูŠ ุนู…ู„ูŠุฉ ุงู„ and ูˆ ุงู„ joint ุนู…ู„ูŠุฉ ุงู„ or ูˆ
68
00:05:26,890 --> 00:05:31,070
ุจู†ุชุฎูŠู„ ุงู† ุงู„ูˆุงุญุฏ ู‡ูˆ ุนุจุงุฑุฉ ุนู† ุงู„ true ูˆ ุงู„ zero
69
00:05:31,070 --> 00:05:36,030
falseูุจูƒูˆู† ุงู„ู„ูŠ ู‡ูŠ ุงู„ .. ุงู„ .. ุงู„ .. ุงู„ .. ุงู„ุฌู…ู„ุฉ
70
00:05:36,030 --> 00:05:40,850
ุงู„ู„ูŠ ููŠู‡ุง ุงู„ู€ and true ุงู„ู„ูŠ ู‡ูŠ ููŠ ุญุงู„ .. ุงู„ .. ุงู„
71
00:05:40,850 --> 00:05:45,590
.. ููŠ ุญุงู„ุฉ ูˆุงุญุฏุฉ ู„ู…ุง ูŠูƒูˆู† ุงู„ุชู…ุชูŠู† true ูŠุนู†ูŠ ุจูƒูˆู†
72
00:05:45,590 --> 00:05:49,210
ูƒู„ู‡ู… false ููŠ ุญุงู„ุฉ ุงู„ู„ูŠ ู‡ูŠ ุงู„ุชู…ุชูŠู† false ุฃูˆ ุฃูŠ
73
00:05:49,210 --> 00:05:53,470
ูˆุงุญุฏุฉ ููŠู‡ู… true ูุจุตูŠุฑ ุนู†ุฏู‰ ุงู„ุขู† ุงู„ูˆุงุญุฏ ูˆูˆุงุญุฏ
74
00:05:53,470 --> 00:05:59,040
ุงู„ูˆุงุญุฏ ู…ูŠุช ุงู„ูˆุงุญุฏ ูˆุงุญุฏูˆ ุงู„ุจุงู‚ู‰ ุงู„ุญุงู„ุงุช ูƒู„ู‡ุง ู‡ูŠุทู„ุน
75
00:05:59,040 --> 00:06:05,040
ุนู†ุฏู‰ ุณูุฑ ุงู„ joint ุงู„ู„ู‰ ู‡ูˆ ุจุชูƒูˆู† ุงู„ู„ู‰ ู‡ูˆ false ูู‰
76
00:06:05,040 --> 00:06:09,560
ุญุงู„ุฉ ูˆุงุญุฏุฉ ู„ู…ุง ู†ูƒูˆู† ุนู†ุฏู‰ ุงู„ุชู†ุชูŠู† false ูˆุจุงู‚ู‰
77
00:06:09,560 --> 00:06:14,200
ุงู„ุญุงู„ุงุช ุงูŠุด ุงุชุฑูˆุง ู„ูƒู† ุงู„ุงู† ุจุนุฏ ุดูˆูŠุฉ ู‡ุนู„ู…ูƒู… ุทุฑูŠู‚ุฉ
78
00:06:14,200 --> 00:06:18,320
ุงู„ู„ู‰ ู‡ูˆ ุงุชุณู‡ู„ ุนู„ูŠูƒู… ุงู„ู„ู‰ ู‡ูˆ ุฅูŠุฌุงุฏ ุงู„ joint ูˆ ุงู„
79
00:06:18,320 --> 00:06:23,560
meet ุจูƒู„ ุณู‡ูˆู„ุฉ ุจุณ ุฎู„ูŠู†ู‰ ุงู„ุงู† ู†ูŠุฌูŠ ู†ุนุฑู ุดูˆ ู…ุนู†ุงุชู‡
80
00:06:23,560 --> 00:06:28,380
ุงู„ joinุจูŠู† ุงู„ู„ูŠ ู‡ูˆ two matrices ูŠุนู†ูŠ ุนู†ุฏ ุงู„ matrix
81
00:06:28,380 --> 00:06:33,900
A ูˆ ุงู„ matrix B ุนุดุงู† ู†ุนู…ู„ู‡ู… join ุจูŠู† ุงู„ A ูˆ ุงู„ B
82
00:06:33,900 --> 00:06:38,620
ู„ุงุฒู… ุฒูŠ ุนู…ู„ูŠุฉ ุงู„ุฌู…ุน ูŠูƒูˆู† ุงู„ู„ูŠ ู‡ูˆ ุงู„ order ู„ู„ุฅุชู†ูŠู†
83
00:06:38,620 --> 00:06:42,600
ุงู„ู„ูŠ ู‡ูŠู† ู†ูุณ ุงู„ order ูŠุนู†ูŠ ู„ูˆ ูƒุงู† ุงู„ A ู…ู† ุงู„ order
84
00:06:42,600 --> 00:06:46,840
on by and ู„ุงุฒู… ูŠูƒูˆู† ุงู„ B ุจุฑุถู‡ ู…ู† ุงู„ order on by
85
00:06:46,840 --> 00:06:51,170
and ูŠุนู†ูŠ ุงู„ู„ูŠ ู‡ูŠู† ู†ูุณ ุงู„ุฏุฑุฌุฉูƒุฐู„ูƒ ุนู…ู„ูŠุฉ ุงู„ู€ meet
86
00:06:51,170 --> 00:06:54,930
ุจุฑุถู‡ ุจูŠู† ุงู„ู€ A ูˆุงู„ู€ BุŒ A ู…ูŠุช B ุจุฑุถู‡ ู„ุงุฒู… ูŠูƒูˆู†
87
00:06:54,930 --> 00:07:00,970
ุงู„ุงุชู†ุชูŠู† ุงู„ู„ูŠ ู‡ู† ุจู†ูุณ ุงู„ุฏุฑุฌุฉ ูˆุนู…ู„ูŠุฉ ุงู„ู„ูŠ ู‡ู‰ ุงู„
88
00:07:00,970 --> 00:07:06,170
meet ุฃูˆ ุงู„ joined ููŠ ุฑูˆุญุฉ ุดุจูŠู‡ุฉ ุจุนู…ู„ูŠุฉ ุงู„ุฌู…ุน ูŠุนู†ูŠ
89
00:07:06,170 --> 00:07:12,290
ูƒู„ ุจู…ุนู†ู‰ ุขุฎุฑ ุฃู†ู‡ ูƒู„ ุนู†ุตุฑ ุจู†ุนู…ู„ู‡ joined ู…ุน ุงู„ุนู†ุตุฑ
90
00:07:12,290 --> 00:07:16,250
ุงู„ู„ูŠ ู…ู‚ุงุจู„ ุฅู„ู‡ ูˆ ุงู„ meet ุจุฑุถู‡ ู†ูุณ ุงู„ุดูŠุก ุฎู„ูŠู†ูŠ ุฃุฎุฏ
91
00:07:16,250 --> 00:07:19,480
ู…ุซุงู„ุŒ ุชุดูˆููˆุง ุงู„ุตู„ุงุฉ ูˆุงู„ู†ุจูŠ ุนู„ูŠู‡ ุงู„ุตู„ุงุฉ ูˆุงู„ุณู„ุงู…ู†ุฌูŠ
92
00:07:19,480 --> 00:07:23,400
ู„ู„ู…ุซุงู„ ุงู„ุฃูˆู„ ุจู‚ูˆู„ find the join and meet of the 0
93
00:07:23,400 --> 00:07:28,440
,1 matrix 0,1 matrices ุงู„ู„ูŠ ุฃู†ุง ุนู†ุฏูŠ ู„ุงู† ููŠ ุนู†ุฏูŠ
94
00:07:28,440 --> 00:07:31,920
ู…ุตููุชูŠู† ู…ุตููˆูุฉ ุงู„ุฃูˆู„ู‰ ูˆุงุถุญ ู…ู† ุงู„ุฏุฑุฌุฉ ูˆุงุญุฏุฉ ุงู„ู„ูŠ ู‡ูŠ
95
00:07:31,920 --> 00:07:36,260
2 ููŠ ุนุฏุฏ ุงู„ุฃุนู†ุงุฏ ุชู„ุงุชุฉ ุงุชู†ูŠู† ููŠ ุชู„ุงุชุฉ ูˆุงู„ุชุงู†ูŠุฉ ุจูŠู‡
96
00:07:36,260 --> 00:07:38,660
ููŠ ุงุชู†ูŠู† ููŠ ุชู„ุงุชุฉ ุงูŠู‡ ุฏู‡ ู…ู† ุงู„ุชู†ูŠู† ู…ู† ู†ูุณ ุงู„ุฏุฑุฌุฉ
97
00:07:38,660 --> 00:07:44,810
ุงุฐุง ุงู„ุฎุทูˆุฉ ุงู„ุฃูˆู„ู‰ ู†ุญูˆ ุงุชุฌุงู‡ ุงู†ู†ุง ู†ุนุฑู ุงู„ุงู„ู„ูŠ ู‡ูŠ
98
00:07:44,810 --> 00:07:50,730
ู…ูˆุฌูˆุฏุฉ ูุฎู„ู‘ูŠู†ูŠ ุงู†ุง ุจู‚ูˆู„ ุงุฐุง join of a and b ุงูŠู‡
99
00:07:50,730 --> 00:07:56,030
join ุจูŠู‡ ุงูŠุด ุจุฏู‡ ุจู†ุงุฎุฏ ูƒู„ ุงู„ entry ู…ุน ุงู„ู„ูŠ ุนุงุฌุจุงู„ู‡
100
00:07:56,030 --> 00:08:00,280
ุนู†ุฏ ุงู„ูˆุงุญุฏ or ุงู„ู„ูŠ ู‡ูˆ mean ุงู„ zeroุฃูˆ join ุงู„ู€ 0 ูˆ
101
00:08:00,280 --> 00:08:04,920
ุงู„ู€ 0 or ุงู„ู€ 1 ูˆ ุงู„ู€ 1 or ุงู„ู€ 0 ู‡ู‰ 1 or ุงู„ู€ 0 ูˆ 0
102
00:08:04,920 --> 00:08:10,680
or ุงู„ู€ 1 ูˆ ู†ูุณ ุงู„ุงุดูŠ 1 or ุงู„ู€ 0 ู‡ู‰ ูˆ ู‡ู†ุง 0 or ุงู„ู€
103
00:08:10,680 --> 00:08:16,640
1 ูˆ ู‡ู†ุง 1 or ุงู„ู€ 1 ูˆ ู‡ู†ุง 0 or ุงู„ู€ 0 ุจุฏู†ุง ู†ุนู…ู„ ู‡ู†ุง
104
00:08:16,640 --> 00:08:22,220
ุงู„ู€ join ู‡ุฐู‡ ุฃุฑูŠุญูƒู… ุงู„ู€ join ุจุณ ุฎุฏ ุงู„ุนุฏุฏ ุงู„ุฃูƒุจุฑ ู…ู†
105
00:08:22,220 --> 00:08:26,100
ู‡ู†ุง ูˆุงุญุฏ ูˆู„ุง ุฒูŠุฑูˆ ู…ู† ุงู„ุนุฏุฏ ูˆุงุญุฏู…ูŠู† ุงู„ุฃูƒุจุฑ ู‡ู†ุงุŸ
106
00:08:26,100 --> 00:08:29,720
ูˆุงุญุฏุŒ ู…ูŠู† ุงู„ุฃูƒุจุฑ ู‡ู†ุงุŸ ูˆุงุญุฏุŒ ู…ูŠู† ุงู„ุฃูƒุจุฑ ู‡ู†ุงุŸ ูˆุงุญุฏุŒ
107
00:08:29,720 --> 00:08:32,080
ู…ูŠู† ุงู„ุฃูƒุจุฑ ู‡ู†ุงุŸ ูˆุงุญุฏุŒ ู…ูŠู† ุงู„ุฃูƒุจุฑ ู‡ู†ุงุŸ ุงู„ู„ูŠ ู‡ูˆ
108
00:08:32,080 --> 00:08:36,660
ุงู„ุณูุฑุŒ ุฅุฐุง ุงู„ join ุงู„ู„ูŠ ู‡ูˆ ุชุงุฎุฏ ุงู„ุฃูƒุจุฑ ููŠู‡ู…ุŒ
109
00:08:36,660 --> 00:08:39,620
ุงู„ุฃูƒุจุฑ ุจูŠู† ุงู„ูˆุงุญุฏ ูˆุจูŠู† ุงู„ุณูุฑ ุฃูˆ ุจูŠู† ุงู„ุณูุฑ ูˆุงู„ุณูุฑ
110
00:08:39,620 --> 00:08:43,480
ุฃูˆ ุจูŠู† ุงู„ูˆุงุญุฏ ูˆุงู„ูˆุงุญุฏุŒ ูˆุงุถุญุฉ ุจุชุตูˆุฑุŒ ู†ูŠุฌูŠ ุงู„ุขู† ุงู„
111
00:08:43,480 --> 00:08:47,000
meetุŒ ุงู„ meet ู…ูŠู† ุงู„ุฃุตุบุฑุŸ ูˆุงู†ุช ุจุชูŠุฌูŠ ุงูŠู‡ุŸุงู„ุงู†
112
00:08:47,000 --> 00:08:50,700
ู…ุงู„ุนุดู†ุง ู†ุณุชุฐูƒุฑ true ูˆ false ูˆ ู…ุด ุนุงุฑู ุงูŠุด ู…ุน ุงู†ู‡
113
00:08:50,700 --> 00:08:55,280
ุณู‡ู„ ุงู„ true ูˆ false ุงู„ู„ูŠ ุจุฏู‡ ุงุญุฏ ุงู„ุทุฑูŠู‚ูŠู† ุงู„ู„ูŠ ู‡ูˆ
114
00:08:55,280 --> 00:09:01,200
ุงุณู‡ู„ูƒู… ุงู„ุงู† the meet of a and b is a meet b a meet
115
00:09:01,200 --> 00:09:05,820
b ุงู„ู„ูŠ ู‡ูˆ ุจูŠุฌูŠ ุงู„ุงู† ู…ุน ูƒู„ ุนู†ุตุฑ a meet zero zero
116
00:09:05,820 --> 00:09:10,960
meet one one meet zero ุงู„ุงู† ู†ูุณ ุงู„ุงุดูŠ zero meet
117
00:09:10,960 --> 00:09:15,990
one one meet oneand zero meet zero ู‡ุงูŠ ุงู„ู„ูŠ ู‡ู†ุง
118
00:09:15,990 --> 00:09:22,170
ุงู„ู„ูŠ ู‡ูŠ a meet b ุงู„ุงู† ุงู„ a meet b ู†ูŠุฌูŠ ู„ู„ูˆุงุญุฏ or
119
00:09:22,170 --> 00:09:24,670
zero ุฒูŠ ู…ุง ู‚ู„ู†ุง ุจุชุงุฎุฏ ุงู„ุตุบูŠุฑ ุจุทู„ุน ุงู„ุตูุฑ ุชุงุฎุฏ
120
00:09:24,670 --> 00:09:27,370
ุงู„ุตุบูŠุฑ ุจุทู„ุน ุงู„ุตูุฑ ุชุงุฎุฏ ุงู„ุตุบูŠุฑ ุจุทู„ุน ุงู„ุตูุฑ ุชุงุฎุฏ
121
00:09:27,370 --> 00:09:30,350
ุงู„ุตุบูŠุฑ ุจุทู„ุน ุงู„ุตูุฑ ูˆู‡ู†ุง ุงู„ุตุบูŠุฑ ูˆุงุญุฏ ุงู„ู„ูŠ ู‡ูˆ ุจูŠู†
122
00:09:30,350 --> 00:09:34,430
ุงู„ูˆุงุญุฏ ูˆุงู„ูˆุงุญุฏ ูˆุงู„ุตุบูŠุฑ ู‡ู†ุง zero ุฃูˆ zero ุฅุฐู† ู‡ุงูŠ
123
00:09:34,430 --> 00:09:39,830
ู…ุนู†ุงุฉ ุงู„ join ุจูŠู† two matrices ูˆู‡ูŠ ู…ุนู†ุงุฉ ุงู„ meet
124
00:09:39,830 --> 00:09:46,100
ุจูŠู† two matricesุงู„ุงู† ุจุฏู†ุง ู†ุนุฑู Boolean product ุงู„ู€
125
00:09:46,100 --> 00:09:49,800
Boolean product ุจูŠู† two matrices ุตู„ูˆุง ุนู„ู‰ ุงู„ู†ุจูŠ
126
00:09:49,800 --> 00:09:53,500
ุนู„ูŠู‡ ุงู„ุตู„ุงุฉ ูˆุงู„ุณู„ุงู… ุงู„ุงู† ุงู„ู€ Boolean product ุจูŠู†
127
00:09:53,500 --> 00:09:59,780
ุงู„ matrix A ูˆ ุงู„ matrix B ุจุฑูˆุญ
128
00:09:59,780 --> 00:10:05,060
ุงู„ุฏุฑุจ ุงู„ุนุงุฏู‰ ู„ูƒู† ุจูˆุงุณุทุฉ ุงู„ join ูˆ ุงู„ meet ูˆ ูƒุฃู†ู‡
129
00:10:05,060 --> 00:10:11,810
ุจุฏู‡ ูŠุตูŠุฑ ุนู†ุฏ ุงู„ meet ุจู„ุนุจุฏูˆุฑ ุงู„ุถุฑุจ ูˆ ุงู„ู€ join ุจู„ุนุจ
130
00:10:11,810 --> 00:10:16,310
ุฏูˆุฑ ุงู„ู„ูŠ ู‡ูˆ ุฅูŠุด ุงู„ุฌู…ุน ุงุชุฎูŠู„ ุฅู†ู‡ ุฃู†ุช ุจุชุถุฑุจ two
131
00:10:16,310 --> 00:10:21,370
matrices ุถุฑุจ ุนุงุฏูŠ ุจุณ ุจุฏู„ ู…ุง ุชุญุท ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุญุท
132
00:10:21,370 --> 00:10:25,930
ุนู…ู„ูŠุฉ ุงู„ู€ join ูˆ ุจุฏู„ ู…ุง ุชุญุท .. ุขุณู ุนู…ู„ูŠุฉ ุงู„ู…ูŠุช ูˆ
133
00:10:25,930 --> 00:10:32,350
ุจุฏู„ ู…ุง ุชุญุท ุนู…ู„ูŠุฉ ุงู„ุฌู…ุน ุญุท ุนู…ู„ูŠุฉ ู…ูŠู† ุงู„ู€ joinู‡ุฏู‰
134
00:10:32,350 --> 00:10:35,850
ูˆู…ุง ุจูŠูƒูˆู†ุด ูˆู„ุง ุฅุด ุฌุฏูŠุฏ ูˆ ุฒู‰ ุงู„ุถุฑุจ ุงู„ุนุงุฏู‰ ุงู„ู„ู‰
135
00:10:35,850 --> 00:10:42,570
ุจู†ุนุฑูู‡ ุจุงู„ุธุจุท ู„ุญุชู‰ ุฃู† ุนุฏุฏ ุงู„ุฏุฑุฌุฉ ุงู„ู€ A ู‡ูŠูƒูˆู† N by
136
00:10:42,570 --> 00:10:48,990
K Matrix ู„ุงุฒู… ุฏุฑุฌุฉ ุงู„ู€ B ูŠูƒูˆู† ู…ู‚ู…ุงู„ู‡ ุงู„ู„ู‰ ู‡ูˆ ูŠุจุฏุฃ
137
00:10:48,990 --> 00:10:55,450
ุจู€ K by N Matrix ูŠุนู†ูŠ ุงู„ุงุชู†ูŠู† ูˆุงู„ุนุฏุฏ ุงู„ุฃูˆู„ุงู†ู‰ ุนุฏุฏ
138
00:10:55,450 --> 00:11:00,360
ุงู„ุฃุนู…ุฏุฉ ุงู„ู„ู‰ ููŠู‡ู„ุงุฒู… ูŠุณุงูˆูŠ ุนุฏุฏ ุงู„ุณุทูˆุฑ ุงู„ู„ูŠ ููŠ ู…ูŠู†
139
00:11:00,360 --> 00:11:05,460
ููŠ ุงู„ู€ matrix ุงู„ู„ูŠ ู‡ูˆ ุงู„ุซุงู†ูŠ ู„ุชุดูˆู ู…ุซุงู„ ุนู…ู„ูŠ
140
00:11:05,460 --> 00:11:09,900
ุฃู…ุงู…ู†ุง ู‡ุฐู‡ ุนู†ุฏ ุงู„ู€ A ูˆู‡ุฐู‡ ุนู†ุฏ ุงู„ู€ B ุจูŠู‚ูˆู„ ู„ูŠ find
141
00:11:09,900 --> 00:11:13,920
the Boolean product of A and B where ุฅุฐุง ุจุฏู†ุง ู†ูˆุฌุฏ
142
00:11:13,920 --> 00:11:18,710
ุงู„ู„ูŠ ู‡ูˆ ุงู„ู€ Boolean productุงู„ู„ูŠ ู‡ูˆ ุจูŠู† ุงู„ู€ A ูˆ ุงู„ู€
143
00:11:18,710 --> 00:11:22,630
B ู…ุงุดูŠ ูŠุง ุฌู…ุงุนุฉ ุทูŠุจ ุงู„ุขู† ุนุดุงู† ูˆุฌูˆุฏ ุงู„ู€ Boolean
144
00:11:22,630 --> 00:11:25,590
Product ุจู…ุด ุจุณุฃู„ ุญุงู„ู†ุง ุฃุตู„ุง ูŠุนู†ูŠ ู‡ุฐุง ู‡ูˆ Zero
145
00:11:25,590 --> 00:11:28,930
Matrix ูˆ ู‡ุฐุง Zero Matrix ุฅุฐุง ุจู†ุญูƒูŠ ูุนู„ุง ุนู† Boolean
146
00:11:28,930 --> 00:11:34,130
Product ุทูŠุจ ู‡ู„ ู‡ุฐุง ุฏุฑุฌุชู‡ ุงู„ู„ูŠ ู‡ูˆ ูˆุงุญุฏุŒ ุงุชู†ูŠู†ุŒ
147
00:11:34,130 --> 00:11:41,580
ุชู„ุงุชุฉ ุตููˆู ุนู…ูˆุฏูŠู†ุŸ ุฃู‡ ูˆ ู‡ุฐุง ู‚ุฏุงุดุŸุงู„ู„ูŠ ู‡ูˆ ุฏุฑุฌุชู‡
148
00:11:41,580 --> 00:11:45,860
ุชู„ุงุชุฉ ููŠ ุงุชู†ูŠู† ูˆู‡ุฐุง ุฏุฑุฌุชู‡ ุงุชู†ูŠู† ููŠ ุชู„ุงุชุฉ ุงุฐุง ุงู„ู„ูŠ
149
00:11:45,860 --> 00:11:50,560
ู‡ูˆ ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุงูŠู‡ ุดู…ุงู„ู‡ุง ุฌุงุฆุฒุฉ ูˆู…ุนุฑูุฉ ุงู„ู€ Boolean
150
00:11:50,560 --> 00:11:55,080
Product ู…ุนุฑู ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ููŠ ู‡ุฐู‡ ุงู„ุญุงู„ุฉ ู†ุดูˆู ูƒูŠู
151
00:11:55,080 --> 00:11:59,830
ู†ูˆุฌุฏู‡ุงุดูˆููˆุง ุนู„ูŠู‡ุง ู„ุฃู† ุจุฏูŠ ุงุฌูŠ ุฒูŠ ู…ุง ู‚ู„ู†ุง ุจุชุฎูŠู„
152
00:11:59,830 --> 00:12:04,710
ุญุงู„ู†ุง ุงู†ู†ุง ุจู†ุถุฑุจ ุถุฑุจ ุนุงุฏูŠ ุจุงุฌูŠ ุนู„ู‰ ุงู„ู„ูŠ ู‡ูˆ ุจุณ ุงู„ู„ูŠ
153
00:12:04,710 --> 00:12:11,770
ู‡ูˆ ุจู†ุบูŠุฑ ุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุจู€Join ูˆุนู…ู„ูŠุฉ ุงู„ู„ูŠ ู‡ูŠ ุงู„ุฌุงู…ุน
154
00:12:11,770 --> 00:12:21,180
ุงุจู†ูŠุชุนู…ู„ูŠุฉ ุงู„ุถุฑุจ ุจู…ูŠุช ูˆุนู…ู„ูŠุฉ ุงู„ุฌู…ุน ุจ join ุจู†ุดูˆู
155
00:12:21,180 --> 00:12:27,200
ูƒูŠู ู„ุฃู† ู†ูŠุฌูŠ ู‡ู†ุง ูˆ ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ุจู†ูŠุฌูŠ ุจู†ู‚ูˆู„ ูˆุงุญุฏ
156
00:12:27,200 --> 00:12:30,240
ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ู…ุน ุงูŠุด ุทุจุนุง ุฒูŠ ู…ุง ุจู†ุนู…ู„ ููŠ ุงู„ุถุฑุจ ู…ุน
157
00:12:30,240 --> 00:12:39,050
ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ ูˆุงุญุฏ ุงุดู…ุงู„ู‡ู…ูŠุช ูˆุงุญุฏ Zero ู…ูŠุช ูˆุงุญุฏ ูˆ
158
00:12:39,050 --> 00:12:43,110
ุจูŠู† ุงู„ุงุชู†ูŠู† ุงูŠุด ู…ุงู„ู‡ ุงู„ join ู‡ุงูŠ ูˆุงุญุฏ ู…ูŠุช ุงู„ูˆุงุญุฏ ูˆ
159
00:12:43,110 --> 00:12:48,670
Zero ู…ูŠุช ุงู„ zero ุงู„ุงู† ุฎู„ุตู†ุง ุงู„ู„ูŠ ู‡ูˆ ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ู…ุน
160
00:12:48,670 --> 00:12:52,430
ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ ุงู„ุงู† ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ู…ุน ู…ูŠู† ู…ุน ุงู„ุนู…ูˆุฏ
161
00:12:52,430 --> 00:13:00,490
ุงู„ุฃูˆู„ ุงู„ุชุงู†ูŠ ุงู„ู„ูŠ ู‡ูˆ ูˆุงุญุฏ ุงู„ู„ูŠ ู‡ูˆ and ุงู„ูˆุงุญุฏูˆ Zero
162
00:13:00,490 --> 00:13:08,550
and ุงู„ูˆุงุญุฏ ูˆ ุจูŠู†ู‡ู…ุง ุนู…ู„ูŠุฉ ุงู„ุงุฑ ูˆู‡ุฐู‡ ู…ูŠุช ูˆู‡ุฐู‡ ุฌูˆูŠู†
163
00:13:08,550 --> 00:13:14,610
ุงู…ูƒู† ู†ู‚ูˆู„ ุฃู†ุฏ ูˆ ุงุฑ ุฃุณู‡ู„ ู„ูƒู… ุงู„ุขู† ุฎู„ุตู†ุง ู…ู† ุงู„ุฌุฒุก
164
00:13:14,610 --> 00:13:20,530
ุงู„ุซุงู†ูŠ ู†ุฌูŠ ู„ู„ุซุงู„ุซ ูˆุงุญุฏ ู…ุน ุงู„ู„ูŠ ู‡ูˆ ุงู„ zero ูˆุงุญุฏ ู…ุน
165
00:13:20,530 --> 00:13:24,850
ุงู„ zero and ูˆ ุงู„ zero ู…ุน ุงู„ ูˆุงุญุฏ and ูˆ ุจูŠู†ู‡ู… ุงูŠุด
166
00:13:24,850 --> 00:13:30,370
ุงุฑุงู„ุงู† ุจู†ุนู…ู„ ู†ูุณ ุงู„ุงุดูŠ ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ู…ุน ุงู„ุนู…ูˆุฏ
167
00:13:30,370 --> 00:13:34,050
ุงู„ุฃูˆู„ ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ุซุงู†ูŠ ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ
168
00:13:34,050 --> 00:13:37,250
ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ุซุงู„ุซ ุจูŠูƒูˆู† ุฌูŠุจู†ุง ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ููŠ
169
00:13:37,250 --> 00:13:41,330
ุงู„ู…ุตู‡ูˆูุฉ ุงู„ู†ุงุชุฌุฉ ู†ูŠุฌูŠ ุงู„ุฃู† ู†ูุณ ุงู„ุงุดูŠ ุงู„ุณุทุฑ ุงู„ุซุงู„ุซ
170
00:13:41,330 --> 00:13:45,570
ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ ุจุชุฌูŠุจ ุงู„ entry ู‡ุฐุง ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ู…ุน
171
00:13:45,570 --> 00:13:49,590
ู‡ุฐุง ุจุชุฌูŠุจ ุงู„ entry ุงู„ู„ูŠ ุจุนุฏู‡ ูˆ ู‡ูƒุฐุง ูุจูƒูˆู† ุงุญู†ุง
172
00:13:49,590 --> 00:13:54,540
ุญุตู„ู†ุง ุนู„ู‰ ุงู„ job ุงู„ู„ูŠ ู‡ูˆ ุงู„ boolean productุงู„ู€
173
00:13:54,540 --> 00:13:59,500
Boolean product ู†ุฏู‰ ุงู„ุงู† ุงู„ู„ู‰ ู‡ูˆ ุนู„ู‰ ุทูˆู„ ู†ุญุณุจ ุงู„ุงู†
174
00:13:59,500 --> 00:14:05,260
ุงู„ ุงู„ ู‚ูˆู„ู†ุง ุงู„ and ุงูŠุด ู…ุงู„ู‡ ู„ุตุบูŠุฑ ูˆุงุญุฏ ูˆ ุงู„ ู‡ู†ุง
175
00:14:05,260 --> 00:14:09,920
ู„ุตุบูŠุฑ ุณูุฑ ุจูŠู†ู‡ู… ุจุฏู†ุง ู†ุงุฎุฏ ุงู„ูƒุจูŠุฑ ุงู„ join ุจุฏู‡
176
00:14:09,920 --> 00:14:13,960
ุงู„ูƒุจูŠุฑ ู‡ุฐุง ูˆุงุญุฏ ูˆู‡ุฐุง ุณูุฑ ุงู„ูƒุจูŠุฑ ูˆุงุญุฏ ู…ุงุดูŠ ุงู„ุญุงู„
177
00:14:13,960 --> 00:14:19,360
ุนู„ู‰ ุทูˆู„ ุงู„ู„ู‰ ุจุนุฏู‡ ู‡ู†ุง ูˆุงุญุฏุงู„ุตุบูŠุฑ ูˆุงุญุฏ ูˆุงู„ุตุบูŠุฑ ู‡ู†ุง
178
00:14:19,360 --> 00:14:24,020
ุณูุฑ ูˆุงุญุฏ ูˆู„ุง ุณูุฑ ุงู„ูƒุจูŠุฑ ู‡ู†ุง ุงู„ join ูƒุจูŠุฑ ู‡ุฐุง ุงู„ or
179
00:14:24,020 --> 00:14:27,600
ูƒุจูŠุฑ ูŠุนู†ูŠ ุจุงุฎุฏ ุตุบูŠุฑ ู‡ุฐู‡ ูˆุตุบูŠุฑ ู‡ุฐู‡ ู…ุน ูƒุจูŠุฑ ุงู„ูƒู„
180
00:14:27,600 --> 00:14:31,860
ุตุบูŠุฑ ู‡ุฐู‡ ูˆุงุญุฏ ูˆุตุบูŠุฑ ู‡ุฐู‡ ุณูุฑ ูƒุจูŠุฑ ู‡ู†ุง ุงู„ุงุชู†ูŠู† ูˆุงุญุฏ
181
00:14:32,420 --> 00:14:36,240
ุงู„ุงู† ุตุบูŠุฑ ู‡ุฐู‡ ุณูุฑ ูˆ ุตุบูŠุฑ ู‡ุฐู‡ ุณูุฑ ูƒุจูŠุฑ ู‡ูŠู† ุงูŠุด
182
00:14:36,240 --> 00:14:42,000
ู‡ูŠุทู„ุน ุณูุฑ ู„ุฃู† ู‡ุฐู‡ ุตุบูŠุฑ ู‡ูŠู† ุณูุฑ ูˆ ู‡ุฐู‡ ุตุบูŠุฑ ู‡ูŠู† ุณูุฑ
183
00:14:42,000 --> 00:14:46,920
ุฅุฐุง ูƒุจูŠุฑ ู‡ูŠู† ุงุชูŠู† ุงุชูŠู† ู„ุงุฒู… ูŠุทู„ุน ุณูุฑ ู„ุฃู† ุงู„ุตุบูŠุฑ
184
00:14:46,920 --> 00:14:51,820
ู‡ุฏูˆู„ุฉ ุณูุฑ ูˆ ูƒุจูŠุฑ ู‡ุฏูˆู„ุฉ ูˆุงุญุฏ ุงู„ุงู† ุตุงุฑ ุนู†ุฏูŠ ุณูุฑ ูˆ
185
00:14:51,820 --> 00:14:56,180
ูˆุงุญุฏ ูƒุจูŠุฑ ู‡ูŠู† ูˆุงุญุฏ ุทุจุนุง ู†ูุณ ุงู„ุงุดูŠ ุตุบูŠุฑ ู‡ูŠู† ุณูุฑ
186
00:14:56,180 --> 00:14:59,620
ู‡ุฏูˆู„ ูˆ ู‡ุฏูˆู„ุฉ ุตุบูŠุฑ ู‡ูŠู† ูˆุงุญุฏ ูƒุจูŠุฑ ุงู„ุฌู‡ุชูŠู† ุงู„ู„ูŠ
187
00:14:59,620 --> 00:15:04,730
ุจูŠุทู„ุนูŠู† ูˆุงุญุฏุงู„ุงู† ุฃุตุบูŠุฑ ู‡ู†ุง ูˆุงุญุฏ ุฃุตุบูŠุฑ ู‡ู†ุง ุณูุฑ
188
00:15:04,730 --> 00:15:11,290
ุฃูƒุจูŠุฑ ุงู„ุฌู‡ุชูŠู† ูˆุงุญุฏ ุฃุตุบูŠุฑ ู‡ู†ุง ูˆุงุญุฏ ูˆ ุฃุตุบูŠุฑ ู‡ู†ุง ุณูุฑ
189
00:15:11,290 --> 00:15:16,770
ุฃูƒุจูŠุฑ ู‡ู†ุง ูˆุงุญุฏ ูุงู‡ู…ูŠู† ุนู„ูŠู‡ุง ุฃุตุบูŠุฑ ู‡ู†ุง ุณูุฑ ูˆ ุฃุตุบูŠุฑ
190
00:15:16,770 --> 00:15:21,990
ู‡ู†ุง ุณูุฑ ุงู„ุณูุฑ ูˆ ุงู„ุณูุฑ ุฃูƒุจูŠุฑ ู‡ู†ุง ุฅูŠุด ุณูุฑ ูˆุงุถุญ ู‡ุฐุง
191
00:15:21,990 --> 00:15:24,370
ุงู„ู„ูŠ ู‡ูˆ ุงู„ boolean of product
192
00:15:26,860 --> 00:15:31,660
ุงู„ุงู† ู†ุงุฎุฏ ู…ุซุงู„ ุงุฎุฑ ู„ุช ุงูŠู‡ ุจุชุณุงูˆูŠ ุงูŠู‡ ุงู„ matrix
193
00:15:31,660 --> 00:15:35,040
ุงู„ู„ูŠ ุงู…ุงู…ูŠ ู‡ุฐุง ุนุจุงุฑุฉ ุนู† matrix ุซู„ุงุซุฉ ููŠ ุซู„ุงุซุฉ ูˆู‚ูˆู„
194
00:15:35,040 --> 00:15:40,280
ู„ูŠ find ู…ุง ูŠู„ูŠู‡ ู…ุงุดูŠ ุงู„ matrices ุงู„ุชุงู„ูŠุฉ ุจุฏูŠ ุงูŠู‡
195
00:15:40,280 --> 00:15:44,740
ุชุฑุจูŠุน ูˆ ุงูŠู‡ ุชูƒุนูŠุฏ ูˆ ุงูŠู‡ ุงุฑุจุนุฉ ูˆ ุงูŠู‡ ุฎู…ุณุฉ ูˆ ุงูŠู‡ n
196
00:15:45,300 --> 00:15:49,680
ุงูŠุด ู…ู‚ุตูˆุฏ ุจุงู„ู€ A ุชุฑุจูŠุน ูŠุนู†ูŠ A Boolean product ู…ุน A
197
00:15:49,680 --> 00:15:54,440
A ุชูƒุนูŠุจ Boolean product A ู…ุน A ู…ุน A ุชู„ุช ู…ุฑุงุช ูŠุนู†ูŠ
198
00:15:54,440 --> 00:15:58,560
A ุชุฑุจูŠุน ู…ุน A ู†ูŠุฏูŠ ู†ุงุฎุฏ ูˆุงุญุฏุฉ ูˆุงุญุฏุฉ ูŠุง ุดุจุงุจ ูˆ ูŠุง
199
00:15:58,560 --> 00:16:02,940
ุจู†ุงุช ุดูˆููˆุง ุตู„ูˆุง ุนู„ู‰ ุงู„ู†ุจูŠ ุนู„ูŠู‡ ุงู„ุตู„ุงุฉ ูˆุงู„ุณู„ุงู… ุนู†ุฏูŠ
200
00:16:02,940 --> 00:16:07,800
ุงู„ A ุงู„ A ุชุฑุจูŠุน ุจุงู„ุณุงูˆูŠุฉ A ุงู„ู„ูŠ ู‡ูˆ ุงู„ Boolean
201
00:16:07,800 --> 00:16:12,570
product ู…ุน ุงู„ AA ุจูˆู„ูŠ ุงู†ุง product ู…ุน ุงู„ู€ A ุงู„ู„ูŠ ู‡ูˆ
202
00:16:12,570 --> 00:16:17,050
ูƒู…ุง ูŠู„ูŠ ุจู†ูŠุฌูŠ ุจู†ุญุท ุงู„ู€ A ู‡ู†ุง ูˆ ุงู„ู€ A ุงู„ุซุงู†ูŠุฉ ููŠ
203
00:16:17,050 --> 00:16:22,910
ู‡ุฐู‡ ุงู„ุฌู‡ุฉ ุงู„ุงู† ุจู†ูŠุฌูŠ ุจู†ุงุฎุฏ ุงู„ุตู ู…ุน ู…ูŠู† ู…ุน ุงู„ุนู…ูˆุฏ
204
00:16:22,910 --> 00:16:28,250
ุงู„ุงู† ุงู„ุตุบูŠุฑ ุงู„ู€ 0 ูˆ ุงู„ู€ 0 ุงู„ู„ูŠ ู…ุน ุจุนุถ ุตุบูŠุฑ ูˆ ุงู„ูƒู„
205
00:16:28,250 --> 00:16:32,430
ุงู„ู„ูŠ ูŠุง ูƒุจูŠุฑูŠุนู†ูŠ ุงู„ุขู† Zero ู…ุน Zero ุตุบูŠุฑู‡ู… Zero
206
00:16:32,430 --> 00:16:36,890
Zero ู…ุน ูˆุงุญุฏ ุตุบูŠุฑู‡ู… Zero ูˆุงุญุฏ ู…ุน ูˆุงุญุฏ ุตุบูŠุฑู‡ู… ูˆุงุญุฏ
207
00:16:36,890 --> 00:16:40,390
ุงุฐุง ูƒุจูŠุฑ ุงู„ุชู„ุงุชุฉ ุงู„ู„ูŠ ู‡ูŠ Zero ูˆ Zero ูˆ ูˆุงุญุฏ ุงู„ู„ูŠ
208
00:16:40,390 --> 00:16:44,120
ู‡ูˆ ู‡ูŠุทู„ุน ูˆุงุญุฏุทูŠุจ ุงู„ู„ูŠ ู…ุง .. ุงู„ู„ูŠ ู…ุง .. ุนุงุฑู ุงู„ู„ูŠ
209
00:16:44,120 --> 00:16:48,500
ู…ุง .. ู…ุงู…ุดูŠุด ู…ุนุงู‡ ูุงุฏู ุชุงู†ูŠุฉ ุงู„ุงู† ุงู„ุณุทุฑ ุงู„ุฃูˆู„ ู…ุน
210
00:16:48,500 --> 00:16:52,620
ุงู„ุนู…ูˆุฏ ุงู„ุชุงู†ูŠ ู…ุงุดูŠ ุงู„ุงู† ุงู„ุณุทุฑ ุงู„ุฃูˆู„ Zero Zero
211
00:16:52,620 --> 00:16:56,360
ุตุบูŠุฑู‡ู† Zero Zero Zero ุตุบูŠุฑู‡ู† Zero ุงู„ูˆุงุญุฏ ูˆ ุงู„ูˆุงุญุฏ
212
00:16:56,360 --> 00:17:00,420
ุตุบูŠุฑู‡ู† ุงู„ูˆุงุญุฏ ุงู„ุงู† ุงูƒุจูŠุฑ ุงู„ุชู„ุงุชุฉ ุงู„ู„ูŠ ุทู„ุน ุงู† ุงู„ู„ูŠ
213
00:17:00,420 --> 00:17:04,620
ุนู†ุฏูŠ ุงู„ุณูุฑ ูˆ ุงู„ุณูุฑ ูˆ ุงู„ูˆุงุญุฏ ูˆุงุญุฏ ูุจุทู„ุน ุนู†ุฏ ุงูŠุด
214
00:17:04,620 --> 00:17:11,430
ุงู„ู„ูŠ ู‡ูˆ ุงู„ู†ุงุชุฌ ูˆุงุญุฏ ู„ุฃู† ุงู„ุนู…ูˆุฏ ู‡ุฐุงุฃุณู ุงู„ุณุทุฑ ู‡ุฐุง
215
00:17:11,430 --> 00:17:15,670
ุงู„ุฃูˆู„ ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ุชุงู„ุช ุงู„ู€ 0 ูˆ ุงู„ู€ 1 ุตุบูŠุฑู‡ู… Zero
216
00:17:15,670 --> 00:17:19,030
ุงู„ู€ 0 ูˆ ุงู„ู€ 0 ุตุบูŠุฑู‡ู… Zero ุงู„ู€ 1 ูˆ ุงู„ู€ 0 ุตุบูŠุฑู‡ู…
217
00:17:19,030 --> 00:17:22,770
Zero ุงู„ู„ูŠ ู‡ู†ุทู„ุน ูƒู„ู‡ ู‡ุฐุง Zero ุฅุฐู† ูƒุจูŠุฑู‡ู… ุฅูŠุด ู‡ูŠุทู„ุน
218
00:17:22,770 --> 00:17:27,550
Zeroุจู†ูุณ ุงู„ุทุฑูŠู‚ุฉ ุจู†ุงุฎุฏ ุงู„ู„ูŠ ู‡ูˆ ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ู…ุน
219
00:17:27,550 --> 00:17:32,570
ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ ูˆุงุญุฏ ู…ุน ุงู„ู€0 ุตุบูŠุฑู‡ู† Zero Zero ู…ุน
220
00:17:32,570 --> 00:17:36,910
ุงู„ูˆุงุญุฏ ุตุบูŠุฑู‡ู† Zero Zero ู…ุน ุงู„ูˆุงุญุฏ ุตุบูŠุฑู‡ู† Zero ุฅุฐุง
221
00:17:36,910 --> 00:17:40,970
ุงู„ุชู„ุงุชุฉ ุตุบูŠุฑุฉ ู‡ู†ุง ู…ุด ู‡ูŠุทู„ุน ุงู„ู„ูŠ ู‡ูˆ ุงู„ู€ Zero ุจู†ูุณ
222
00:17:40,970 --> 00:17:45,130
ุงู„ุฃุณู„ูˆุจ ุจู†ุทู„ุน ุจุงู‚ูŠ ุงู„ู„ูŠ ู‡ูŠ ุงู„ู‚ูŠู… ูุจูƒูˆู† ุนู†ุฏู‰ ุจุทู„ุน
223
00:17:45,130 --> 00:17:48,950
ุงู„ matrix ู‡ุฐุง ุงู„ู„ูŠ ุฃู…ุงู…ู‰ู„ุฃู† ู‡ุฐุง ุงู„ู€ matrix ุงู„ู„ูŠ
224
00:17:48,950 --> 00:17:52,130
ุฃู…ุงู…ูŠ ู‡ูˆ ุงู„ู€ A ุชุฑุจูŠุน ุจุฏูŠ ุฃูˆุฌุฏ ุงู„ู€ A ุชูƒุนูŠุจ ุงู„ู€ A
225
00:17:52,130 --> 00:17:55,350
ุชูƒุนูŠุจ ุฅูŠุด ู‡ุชุณุงูˆูŠ ุงู„ู€ A ุชุฑุจูŠุน ุงู„ู„ูŠ ุทู„ุน ู‡ุฐุง ู‡ูŠูˆ
226
00:17:55,350 --> 00:18:00,050
ุฌุจุชู‡ุงู† ุฏุฑู‚ ุงู„ู„ูŠ ู‡ูˆ Boolean product ู…ุน ู…ูŠู† ู…ุน ุงู„ู€ A
227
00:18:00,050 --> 00:18:04,190
ุงู„ู„ูŠ ู‡ูˆ ุงู„ุฃุตู„ ู‡ูŠูˆ ู†ูŠุฏูŠ ู†ุถุฑุจู‡ู… ู…ุน ุจุนุถ ุฒูŠ ู…ุง ู‚ู„ู†ุง
228
00:18:04,190 --> 00:18:08,450
ู‚ุจู„ ุจุดูˆูŠุฉ ูˆุงุญุฏ ูˆ Zero ุตุบูŠุฑ ู…ู† Zero ูˆุงุญุฏ ูˆุงุญุฏ ุตุบูŠุฑ
229
00:18:08,450 --> 00:18:13,090
ู…ู† ูˆุงุญุฏ ุฎู„ุงุต ู…ุฏุงู… ุทู„ุน ู‡ู†ุง ูˆุงุญุฏ ููŠ ุงู„ุตุบุงุฑ ูˆุงุญุฏ ุฅุฐุง
230
00:18:13,090 --> 00:18:17,780
ุนู„ู‰ ุทูˆู„ ุงู„ูƒุจุงุฑ ู‡ูŠุทู„ุน ุจูŠู†ู‡ู† ุฅูŠุด ูˆุงุญุฏู…ุงูƒู…ู„ุด ูŠุนู†ูŠ ู„ุฅู†
231
00:18:17,780 --> 00:18:22,880
ู‡ุฐุง ุงู„ุณุทุฑ ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ุซุงู†ูŠ ู„ุฅู† ูˆุงุญุฏ ู…ุน ุงู„ zero
232
00:18:22,880 --> 00:18:26,020
zero ูˆุงุญุฏ ู…ุน ุงู„ zero zero ุงู„ุตุบูŠุฑ ุทุจุนุง zero ู…ุน ุงู„
233
00:18:26,020 --> 00:18:29,000
zero zero ุฏู‡ ู†ุทู„ุน ูƒู„ู‡ ู†ุตูุงุฑ ุฏู‡ ู‡ูŠุทู„ุน ุงู„ูƒุจูŠุฑ zero
234
00:18:29,000 --> 00:18:32,800
ู„ุฅู† ูˆุงุญุฏ ู…ุน ุงู„ูˆุงุญุฏ ุทู„ุน ูˆุงุญุฏ ู…ุซู„ุง ูˆุงุญุฏ ุทู„ุน ูˆุงุญุฏ ู…ู†
235
00:18:32,800 --> 00:18:36,260
ุนู…ู„ูŠุฉ ุงู„ู„ูŠ ู‡ูˆ ู…ูŠู† ุตุบูŠุฑู‡ู… ู‡ุฐุง ุงู„ู„ูŠ ู…ุงุฎุฏุช ู…ูŠู† ูŠุง
236
00:18:36,260 --> 00:18:40,090
ุฌู…ุงุนุฉ ุงู„ู„ูŠ ู…ุงุฎุฏุชูŠ ุงู„ุนู…ูˆุฏ ุงู„ุณุทุฑ ุงู„ุฃูˆู„ู…ุน ุงู„ุนู…ูˆุฏ
237
00:18:40,090 --> 00:18:43,830
ุงู„ุชุงู„ุช ูˆุงุญุฏ ู…ุน ูˆุงุญุฏ ู„ุตุบูŠุฑ ูˆุงุญุฏ ุฅุฐุง ู…ุง ูŠุทู„ุน ุงู„ูƒุจูŠุฑ
238
00:18:43,830 --> 00:18:45,770
ู‡ู†ุง ุฅูŠุด ู…ุง ูŠุทู„ุน ู…ู† ุงู„ุจุงู‚ูŠุช ู‡ูŠุทู„ุน ุงู„ูƒุจูŠุฑ ู‡ู†ุง ูˆุงุญุฏ
239
00:18:45,770 --> 00:18:50,110
ู‡ุงูŠ ูˆุงุญุฏ ูˆุจุนุฏูŠ ุจุนู…ู„ ุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ุจู†ูุณ ุงู„ุฃุณู„ูˆุจ ู…ุน
240
00:18:50,110 --> 00:18:53,730
ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ ูˆุงู„ุณุทุฑ ุงู„ุซุงู†ูŠ ุจุญุตู„ ุนู„ู‰ ุงู„ matrix ุงู„ู„ูŠ
241
00:18:53,730 --> 00:18:57,450
ุฃู…ุงู…ู†ูŠ ุงู„ู„ูŠ ู‡ูˆ ู‡ุฐุง ู‡ุฐุง ุงู„ู„ูŠ ุทู„ุน ู…ูŠู† ุนู†ุฏูŠ a ุชูƒุนูŠุจ
242
00:18:57,450 --> 00:19:01,910
ุชุนุงู„ูŠ ุงู„ a ุชูƒุนูŠุจ ู‡ุฐุง ุจุฏูŠ ุฃุถุฑุจู‡ ููŠ ุงู„ a ุจุทู„ุน ู…ูŠู† a
243
00:19:01,910 --> 00:19:04,810
ู‚ุตุฉ ุฃุฑุจุนุฉ ูŠุนู†ูŠ ุงูŠู‡ ุจุฏูŠ a ุฃุฑุจุนุฉ ุจุณุงูˆูŠ a ุชูƒุนูŠุจ ุงู„ู„ูŠ
244
00:19:04,810 --> 00:19:08,610
ุทู„ุนุชู‡ ู…ู† ุงู„ุฎุทูˆุฉ ู‡ุฐู‡ ููŠ a ู‡ุงูŠู‡ a ุชูƒุนูŠุจ ูˆู‡ูŠู‡ ุงู„ a
245
00:19:09,070 --> 00:19:15,490
ู„ุงุญุธ ุงู„ุขู† ูˆุงุญุฏ ู…ุน ุงู„ู€ 00 ุจุงู„ุตุบูŠุฑุŒ Zero ู…ุน ุงู„ุณุทุฑ
246
00:19:15,490 --> 00:19:19,410
ุงู„ุฃูˆู„ ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ุฃูˆู„ุŒ ู†ุนูŠุฏ ู†ูุณ ุงู„ูƒู„ุงู…ุŒ ูˆุงุญุฏ ู…ุน
247
00:19:19,410 --> 00:19:23,230
ุงู„ู€ 00ุŒ Zero ู…ุน ุงู„ูˆุงุญุฏุŒ ZeroุŒ ูˆุงุญุฏ ู…ุน ุงู„ูˆุงุญุฏุŒ
248
00:19:23,230 --> 00:19:27,290
ูˆุงุญุฏุŒ ุฏู‡ ู†ุทู„ุน ูˆุงุญุฏุŒ ุงู„ุขู† ุงู„ู„ูŠ ุจุนุฏู‡ุŒ ู‡ุฐุง ุงู„ุณุทุฑ ู…ุน
249
00:19:27,290 --> 00:19:30,410
ู‡ุฐุง ุงู„ุนู…ูˆุฏุŒ ู„ุงุญุธูˆุง ุฃู†ู‡ ู‡ูŠุชุฌูŠ ุงู„ูˆุงุญุฏ ู‡ุฐุง ู…ุน ุงู„ูˆุงุญุฏุŒ
250
00:19:30,410 --> 00:19:33,610
ุฏู‡ ู‡ูŠุทู„ุน ูˆุงุญุฏ ู…ู†ู‡ุŒ ุฏู‡ ู‡ูŠุทู„ุน ุงู„ูƒู„ ุฅูŠู‡ ุดู…ุงู„ู‡ุŸ ูˆุงุญุฏ
251
00:19:33,810 --> 00:19:38,370
ู†ุฌูŠ ู„ู‡ุฐุง ู‡ูŠู„ุชุฌูŠ ู…ุน ู‡ุฐุง ู…ุน ุงู„ูˆุงุญุฏ ู…ุงุฏุงู… ูˆุงุญุฏ ุงู„ุชุฌู‡
252
00:19:38,370 --> 00:19:41,870
ู…ุน ุงู„ูˆุงุญุฏ ุฅุฐุง ุฃุตุบูŠุฑ ุงู„ูˆุงุญุฏูŠู† ูˆุงุญุฏ ุฅุฐุง ุงู„ูƒุจูŠุฑ
253
00:19:41,870 --> 00:19:46,750
ุงู„ู†ุงุชุฌ ุจูŠุทู„ุน ุฅูŠุด ูˆุงุญุฏ ุฅุฐุง ู‡ุฐุง ูƒู„ ูˆุงุญุฏ ุฏู‡ ู‡ุฌุฑุจ ู‡ุฐุง
254
00:19:46,750 --> 00:19:50,530
ู…ุน ู‡ุฐุง ุจุฑุถู‡ ู†ูุณ ุงู„ุงุดูŠ ูˆุงุญุฏ ู…ุน Zero Zero ูˆุงุญุฏ ู…ุน
255
00:19:50,530 --> 00:19:53,150
ูˆุงุญุฏ ูˆุงุญุฏ ุจุฒู† ุทู„ุน ูˆุงุญุฏ ุนู„ู‰ ุทูˆู„ ุจูŠุทู„ุน ุฅูŠุด ู‡ุฐุง ุนู†ุฏ
256
00:19:53,150 --> 00:19:57,070
ูˆุงุญุฏ ุจูƒู…ู„ ุนู…ู„ูŠุฉ ุงู„ุฏุฑุจ ู‡ูŠุทู„ุน ุนู†ุฏ ุงู„ matrix ุงู„ุฃู…ุงู…ูŠ
257
00:19:57,070 --> 00:20:00,290
ู‡ุฐุง ูƒู„ ูˆุงุญุฏุงุช ู…ุน ู‡ุฐุง ุงู„ู„ูŠ ููŠ ุงู„ู†ุต Zero ุทูŠุจ ุดูˆู ุฅูŠุด
258
00:20:00,290 --> 00:20:05,350
ุงู„ู„ูŠ .. ุฅูŠุด ุงู„ู„ูŠ ุจุฏู†ุง ู‡ูŠุชุนุงู„ ุฎุฏ a5 a5 ุนุจุงุฑุฉ ุนู† ุงูŠุด
259
00:20:05,350 --> 00:20:15,990
ูŠุง ุฌู…ุงุนุฉ a5 ู‡ูŠ a5 ุงู„ู„ูŠ ุนู†ุฏูƒ ู…ุงุดูŠ ุทูŠุจ a5 ุดูˆู
260
00:20:15,990 --> 00:20:21,670
ู‡ูŠ a5 a5 ุจุณูˆุก a4 ููŠ a a4 ู‡ูŠ ุงู„ู„ูŠ ุฌูŠุจุชู‡ ู…ู†ู‡ุง ู‡ูŠ a4
261
00:20:21,670 --> 00:20:26,610
ูŠุง ุดุจุงุจู…ุงุดูŠ ู‡ูŠู† ุญุทูŠุชู‡ ู‡ุงู† ูˆู‡ูŠ ู‡ุฐุง ุงู„ู€ A ุงู„ุฃุตู„ูŠ ุงู„ู€
262
00:20:26,610 --> 00:20:31,310
D ุงุชุถุฑุจุช ู‡ู„ุฌูŠุช ุงู„ูˆุงุญุฏ ู…ุน ุงู„ zero ุงู„ู„ูŠ ู‡ูˆ zero ู„ุฃู†ู‡
263
00:20:31,310 --> 00:20:34,030
ู„ุตุบูŠุฑ ุจู†ุงุฎุฏ ูˆุงุญุฏ ู…ุน ุงู„ูˆุงุญุฏ ูˆุงุญุฏ ู…ุฏุงู… ุทู„ุน ูˆุงุญุฏ ุฒูŠ
264
00:20:34,030 --> 00:20:38,470
ู…ุง ู‚ู„ู†ุง ุจูŠุทู„ุน ูƒุจูŠุฑ ุงู„ู†ุงุชุฌ ูˆุงุญุฏ ุงู„ุงู† ุชุนุงู„ูŠ ู…ุน ู‡ุฐุง
265
00:20:38,470 --> 00:20:42,250
ุงู„ุณุทุฑ ู…ุน ู‡ุฐุง ู‡ูŠู„ุชู‚ูŠ ุงูƒูŠุฏ ูˆุงุญุฏ ู…ุน ูˆุงุญุฏ ู…ุฏุงู… ุงู„ุชู‚ู‰
266
00:20:42,250 --> 00:20:45,370
ูˆุงุญุฏ ู…ุน ูˆุงุญุฏ ุงุฐุง ุงู†ุง ุตุบูŠุฑ ู‡ู†ุง ูˆุงุญุฏ ุงุฐุง ูƒุจูŠุฑ ุงู„ูƒู„
267
00:20:45,370 --> 00:20:48,350
ุจูŠุตูŠุฑ ุงุดู…ุงู„ ู‡ูˆ ุจูŠุตูŠุฑ ูˆุงุญุฏ ุจูŠุทู„ุน ุงู„ entry ู‡ุฐุง ูˆุงุญุฏ
268
00:20:48,760 --> 00:20:52,680
ุงู„ุงู† ุงู„ู„ูŠ ู…ุด ูุงู‡ู… ุนู„ูŠุง ูŠุนู†ูŠ ูŠุถุฑุจ ุถุฑุจ ูˆุงุญุฏุฉ ูˆุงุญุฏุฉ
269
00:20:52,680 --> 00:20:57,020
ู„ูƒู† ุจุตูˆุฑ ุงู„ูƒู„ุงู… ูˆุงุถุญ ุงู„ุงู† ู‡ุฐุง ุงู„ุณุทุฑ ู…ุน ุงู„ุนู…ูˆุฏ ุงู„ู„ูŠ
270
00:20:57,020 --> 00:21:01,780
ู‡ูˆ ุงู„ุงุด ุงู„ุฃุฎูŠุฑ ุงู„ุณุทุฑ ู‡ุฐุง ูˆุงุญุฏ ู…ุน ุงู„ูˆุงุญุฏ ูˆุงุญุฏ ูŠุนู†ูŠ
271
00:21:01,780 --> 00:21:06,640
ู„ุฅู†ู‡ ุตุบูŠุฑ ูˆุงุญุฏ ุงู„ุงู† ู…ุงูƒู…ู„ุด ุงู„ุถุฑุจ ู„ุฅู†ู‡ ู„ู…ุง ุจุฏูŠ ุฃุฎุฏ
272
00:21:06,640 --> 00:21:10,140
ูƒุจูŠุฑ ุงู„ู†ุงุชุฌ ูˆุนู†ุฏูŠ ูˆุงุญุฏ ุทู„ุน ูˆุงุญุฏ ุฅุฐุง ูƒุจูŠุฑ ุงู„ู†ุงุชุฌ
273
00:21:10,140 --> 00:21:15,420
ู‡ูŠุทู„ุน ุงุด ูˆุงุญุฏุงู„ุงู† ู‡ุฐุง ุจูƒู…ู„ู‡ ู…ุน ู‡ุฐุง ูˆ ุจูƒู…ู„ู‡ ู…ุน ู‡ุฐุง
274
00:21:15,420 --> 00:21:18,440
ูˆ ุจูƒู…ู„ู‡ ู…ุน ู‡ุฐุง ุจุทู„ุน ุนู†ุฏูŠ ุงู„ matrix ุงู„ุฃู…ุงู…ูŠ ุจุทู„ุน
275
00:21:18,440 --> 00:21:23,760
ุนู†ุฏูŠ A5 ุงูŠุด ุจุณุงูˆูŠ ุจุณุงูˆูŠ ูˆุงุญุฏ ุงู„ุงู† ุจุนุฏ ู‡ูŠูƒ ู„ูˆ ุฌูŠุช
276
00:21:23,760 --> 00:21:27,720
ุถุฑุจุช ุฌูŠุจุช A6 ูŠุนู†ูŠ ุฌูŠุจุช ุงู„ matrix ุงู„ุฃุตู„ูŠ ู‡ุฐุง ูˆ
277
00:21:27,720 --> 00:21:31,330
ุถุฑุจุชู‡ ููŠ ุงู„ ู‡ุฐุง ุงู„ู„ูŠ ุทู„ุน ูˆุญุฏุงุชู‚ุทุนุง ุงู„ูˆุญุฏุงุช ู‡ูŠุชุฌุงุจู„
278
00:21:31,330 --> 00:21:37,830
ู…ุน ุงู„ู„ุบุงุช ูู‡ูŠุนู…ู„ู† ูƒู„ ูˆุญุฏุงุช ุงุฐุง ุงู„ุงู† ุฌุฑุจ A5 ู…ุน A ูˆ
279
00:21:37,830 --> 00:21:41,990
ุถุฑุจู‡ุง ุจูŠุทู„ุน ุนู†ุฏูƒ A6 ู‡ูŠุทู„ุน ูˆุงุญุฏ ูˆุงุญุฏ ูˆุงุญุฏ ูƒู„ ูˆุงุญุฏ ูˆ
280
00:21:41,990 --> 00:21:45,730
ู‡ูŠุธู„ูˆุง ูŠุทู„ุน ุนู†ุฏูƒ ูˆุงุญุฏ ุงู„ู„ูŠ ู‡ูˆ ุงู„ matrix ู‡ุฐุง ุนู„ู‰
281
00:21:45,730 --> 00:21:50,440
ุทูˆู„ ุจุงู„ุดูƒู„ ู‡ุฐุงู‡ุฐู‡ ุงู„ุขู† ุงู„ู„ูŠ ู‡ูŠ ุนู…ู„ูŠุฉ ุงู„ boolean
282
00:21:50,440 --> 00:21:54,920
ุงู„ู„ูŠ ู‡ูˆ operation ุฃูˆ ุงู„ .. ุงู„ .. ุงู„ boolean
283
00:21:54,920 --> 00:21:59,560
product ุงู„ู„ูŠ .. ุงู„ู„ูŠ ู‡ูŠ ุฒูŠ ู…ุง ู‚ู„ู†ุง ููŠ ุงู„ู…ุญุงุถุฑุฉ
284
00:21:59,560 --> 00:22:04,280
ุงู„ู„ูŠ ู‡ูŠ ุงู„ boolean operation ู‡ูŠ ููŠ ุงู„ูˆุงู‚ุน ุงู„ or ูˆ
285
00:22:04,280 --> 00:22:08,480
ุงู„ and ุจุชุนู…ู„ ุญุงุฌุฉ ุงุณู…ู‡ุง boolean algebra ู…ุด ู…ูˆุถูˆุนู†ุง
286
00:22:08,480 --> 00:22:17,520
ู„ูƒู† ู„ู„ูŠ ุจุฏูˆุง ูŠุนุฑูุงู„ุงู† ุงู†ุชู‡ุช ุงู„ุฌุฒุก ุงู„ุฃูˆู„ ู…ู† ู…ุญุงุถุฑุฉ
287
00:22:17,520 --> 00:22:23,500
ุงู„ู€ matrices ูƒูƒู„ ุงู„ู…ุทู„ูˆุจ
288
00:22:23,500 --> 00:22:27,460
ู…ู†ูƒู… ุงู† ูŠูƒูˆู† ุนู†ุฏ ุงู„ matrix ู‡ุฐุง ุงู„ matrix B ูˆู‡ูŠ ุงู„
289
00:22:27,460 --> 00:22:31,590
matrix ุงู„ identity matrixุจุฏูŠ ุชูˆุฌุฏูˆู„ูŠ ุงู„ู„ูŠ ู‡ูˆ ุงู„ a
290
00:22:31,590 --> 00:22:35,490
ุชุฑุจูŠุน ูˆ ุงู„ a ุชูƒุนูŠุจ ูˆ ุงู„ a n ู„ูƒู„ n greater than or
291
00:22:35,490 --> 00:22:39,490
equal to 3 ูˆ ุชูˆุฌุฏูˆู„ูŠ ุงู„ุจูˆู„ูŠู† ุงู„ product ุจูŠู† ุงู„ a ูˆ
292
00:22:39,490 --> 00:22:43,090
ุงู„ b ูˆ ุงู„ุจูˆู„ูŠู† ุงู„ product ุจูŠู† ุงู„ a ูˆ ุงู„ c ูˆ ู‡ุฐูˆู„ุฉ
293
00:22:43,090 --> 00:22:46,830
ุงู„ู„ูŠ ู‡ู‰ ู‡ุฐุง ุงู„ุณุคุงู„ ุจุณ ู‡ู‰ ุงู„ุณุคุงู„ ู‡ุฐุง ุงู„ู„ูŠ ู‡ูˆ ุงู„ a ูˆ
294
00:22:46,830 --> 00:22:50,930
ุงู„ b ูˆ ุงู„ i ูˆ ู‡ุฐูˆู„ุฉ ูˆ ู‡ุฐูˆู„ุฉ ุจุฏูŠ ุชูˆุฌุฏูˆู„ูŠู‡ุง ูˆ
295
00:22:50,930 --> 00:22:55,210
ุชุนู…ู„ูˆู„ูŠู‡ุง ูˆ ุชูƒุชุจูˆู„ูŠู‡ุงููŠ homework ูˆ ุฒูŠ ุงู„ homework
296
00:22:55,210 --> 00:22:59,770
ุงู„ู„ูŠ ูุงุช ูˆ ุชุจุนุชูˆู„ูŠู‡ ุนู„ู‰ ุงู„ู„ูŠ ู‡ูˆ ุงู„ whats ุงูˆ ุนู„ู‰ ุงู„
297
00:22:59,770 --> 00:23:04,990
model ุฒูŠ ู…ุง ุจุฏูƒู… ุฒูŠ ู…ุง ุจุชุดูˆููˆุง ู…ู†ุงุณุจ ูˆ ุงู† ุดุงุก ุงู„ู„ู‡
298
00:23:04,990 --> 00:23:10,470
ููŠ ู„ู‚ุงุก ุงุฎุฑ ุจูŠู†ูƒู…ู„ ุงู„ู„ูŠ ู‡ูˆ ุงู„ determinants ุงูˆ
299
00:23:10,470 --> 00:23:14,170
ุงู„ู…ุญุฏุฏุงุช ูˆุงู„ุณู„ุงู… ุนู„ูŠูƒู… ูˆุฑุญู…ุฉ ุงู„ู„ู‡ ูˆุจุฑูƒุงุชู‡