[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.67,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.67,0:00:02.38,Default,,0000,0000,0000,,Well, after the last video,\Nhopefully, we're a little
Dialogue: 0,0:00:02.38,0:00:04.33,Default,,0000,0000,0000,,familiar with how you\Nadd matrices.
Dialogue: 0,0:00:04.33,0:00:07.15,Default,,0000,0000,0000,,So now let's learn how\Nto multiply matrices.
Dialogue: 0,0:00:07.15,0:00:11.45,Default,,0000,0000,0000,,And keep in mind, these are\Nhuman-created definitions for
Dialogue: 0,0:00:11.45,0:00:12.84,Default,,0000,0000,0000,,matrix multiplication.
Dialogue: 0,0:00:12.84,0:00:15.00,Default,,0000,0000,0000,,We could have come up with\Ncompletely different ways to
Dialogue: 0,0:00:15.00,0:00:15.45,Default,,0000,0000,0000,,multiply it.
Dialogue: 0,0:00:15.45,0:00:18.51,Default,,0000,0000,0000,,But I encourage you to learn\Nthis way because it'll help
Dialogue: 0,0:00:18.51,0:00:19.81,Default,,0000,0000,0000,,you in math class.
Dialogue: 0,0:00:19.81,0:00:22.10,Default,,0000,0000,0000,,And we will see later that\Nthere's actually a lot of
Dialogue: 0,0:00:22.10,0:00:24.73,Default,,0000,0000,0000,,applications that come out\Nof this type of matrix
Dialogue: 0,0:00:24.73,0:00:25.29,Default,,0000,0000,0000,,multiplication.
Dialogue: 0,0:00:25.29,0:00:26.34,Default,,0000,0000,0000,,So let me think of\Ntwo matrices.
Dialogue: 0,0:00:26.34,0:00:30.32,Default,,0000,0000,0000,,I will do two 2 by 2 matrices,\Nand let's multiply them.
Dialogue: 0,0:00:30.32,0:00:34.50,Default,,0000,0000,0000,,Let's say-- let me pick some\Nrandom numbers: 2,
Dialogue: 0,0:00:34.50,0:00:40.53,Default,,0000,0000,0000,,minus 3, 7, and 5.
Dialogue: 0,0:00:40.53,0:00:42.98,Default,,0000,0000,0000,,And I'm going to multiply that\Nmatrix, or that table of
Dialogue: 0,0:00:42.98,0:00:56.44,Default,,0000,0000,0000,,numbers, times 10, minus 8--\Nlet me pick a good number
Dialogue: 0,0:00:56.44,0:01:03.98,Default,,0000,0000,0000,,here-- 12, and then minus 2.
Dialogue: 0,0:01:03.98,0:01:07.40,Default,,0000,0000,0000,,So now there might be a strong\Ntemptation-- and you know in
Dialogue: 0,0:01:07.40,0:01:11.33,Default,,0000,0000,0000,,some ways it's not even an\Nillegitimate temptation-- to
Dialogue: 0,0:01:11.33,0:01:13.88,Default,,0000,0000,0000,,do the same thing with\Nmultiplication that we did
Dialogue: 0,0:01:13.88,0:01:17.52,Default,,0000,0000,0000,,with addition, to just multiply\Nthe corresponding
Dialogue: 0,0:01:17.52,0:01:20.58,Default,,0000,0000,0000,,terms. So you might be tempted\Nto say, well, the first term
Dialogue: 0,0:01:20.58,0:01:23.16,Default,,0000,0000,0000,,right here, the 1, 1 term, or\Nin the first row and first
Dialogue: 0,0:01:23.16,0:01:25.07,Default,,0000,0000,0000,,column, is going to\Nbe 2 times 10.
Dialogue: 0,0:01:25.07,0:01:26.97,Default,,0000,0000,0000,,And this term is going\Nto be minus 3 times
Dialogue: 0,0:01:26.97,0:01:28.23,Default,,0000,0000,0000,,minus 8 and so forth.
Dialogue: 0,0:01:28.23,0:01:30.33,Default,,0000,0000,0000,,And that's how we added matrices\Nso maybe it's a
Dialogue: 0,0:01:30.33,0:01:33.51,Default,,0000,0000,0000,,natural extension to multiply\Nmatrices the same way.
Dialogue: 0,0:01:33.51,0:01:36.18,Default,,0000,0000,0000,,And that is legitimate.
Dialogue: 0,0:01:36.18,0:01:38.53,Default,,0000,0000,0000,,One could define it that way,\Nbut that's not the way it is
Dialogue: 0,0:01:38.53,0:01:39.41,Default,,0000,0000,0000,,in the real world.
Dialogue: 0,0:01:39.41,0:01:40.38,Default,,0000,0000,0000,,And the way in the real world,
Dialogue: 0,0:01:40.38,0:01:42.47,Default,,0000,0000,0000,,unfortunately, is more complex.
Dialogue: 0,0:01:42.47,0:01:44.98,Default,,0000,0000,0000,,But if you look at a\Nbunch of examples I
Dialogue: 0,0:01:44.98,0:01:45.67,Default,,0000,0000,0000,,think you'll get it.
Dialogue: 0,0:01:45.67,0:01:47.46,Default,,0000,0000,0000,,And you'll learn that\Nit's actually fairly
Dialogue: 0,0:01:47.46,0:01:47.98,Default,,0000,0000,0000,,straightforward.
Dialogue: 0,0:01:47.98,0:01:48.98,Default,,0000,0000,0000,,So how do we do it?
Dialogue: 0,0:01:48.98,0:01:53.29,Default,,0000,0000,0000,,So this first term that's in\Nthe first row and its first
Dialogue: 0,0:01:53.29,0:01:58.05,Default,,0000,0000,0000,,column, is equal to essentially\Nthis first row's
Dialogue: 0,0:01:58.05,0:02:01.38,Default,,0000,0000,0000,,vector-- no, this first\Nrow vector--
Dialogue: 0,0:02:01.38,0:02:04.79,Default,,0000,0000,0000,,times this column vector.
Dialogue: 0,0:02:04.79,0:02:08.23,Default,,0000,0000,0000,,Now what do I mean\Nby that, right?
Dialogue: 0,0:02:08.23,0:02:11.32,Default,,0000,0000,0000,,So it's getting it's row\Ninformation from the first
Dialogue: 0,0:02:11.32,0:02:14.17,Default,,0000,0000,0000,,matrix's row, and it's getting\Nit's column information from
Dialogue: 0,0:02:14.17,0:02:16.32,Default,,0000,0000,0000,,the second matrix's column.
Dialogue: 0,0:02:16.32,0:02:17.19,Default,,0000,0000,0000,,So how do I do that?
Dialogue: 0,0:02:17.19,0:02:18.86,Default,,0000,0000,0000,,If you're familiar with dot\Nproduct, it's essentially the
Dialogue: 0,0:02:18.86,0:02:20.93,Default,,0000,0000,0000,,dot product of these\Ntwo matrices.
Dialogue: 0,0:02:20.93,0:02:24.82,Default,,0000,0000,0000,,Or without saying it that fancy,\Nit's just this: it's 2
Dialogue: 0,0:02:24.82,0:02:31.89,Default,,0000,0000,0000,,times 10, so 2-- I'm going to\Nwrite small-- times 10, plus
Dialogue: 0,0:02:31.89,0:02:39.64,Default,,0000,0000,0000,,minus 3 times 12.
Dialogue: 0,0:02:39.64,0:02:42.63,Default,,0000,0000,0000,,I'm going to run out of space.
Dialogue: 0,0:02:42.63,0:02:45.60,Default,,0000,0000,0000,,And so what's this second\Nterm over here?
Dialogue: 0,0:02:45.60,0:02:49.17,Default,,0000,0000,0000,,Well, we're still on the first\Nrow of the product vector but
Dialogue: 0,0:02:49.17,0:02:50.35,Default,,0000,0000,0000,,now we're on the\Nsecond column.
Dialogue: 0,0:02:50.35,0:02:51.91,Default,,0000,0000,0000,,We get our column information\Nfrom here.
Dialogue: 0,0:02:51.91,0:02:58.80,Default,,0000,0000,0000,,So let's pick a good color--\Nthis is a slightly different
Dialogue: 0,0:02:58.80,0:03:00.53,Default,,0000,0000,0000,,shade of purple.
Dialogue: 0,0:03:00.53,0:03:04.11,Default,,0000,0000,0000,,So now this is going to be--\NI'll do that in another
Dialogue: 0,0:03:04.11,0:03:10.58,Default,,0000,0000,0000,,color-- 2 times minus 8-- let me\Njust write out the number--
Dialogue: 0,0:03:10.58,0:03:18.81,Default,,0000,0000,0000,,2 times minus 8 is minus 16,\Nplus minus 3 times minus 2--
Dialogue: 0,0:03:18.81,0:03:21.16,Default,,0000,0000,0000,,what's minus 3 times minus 2?
Dialogue: 0,0:03:21.16,0:03:26.40,Default,,0000,0000,0000,,That is plus 6, right?
Dialogue: 0,0:03:26.40,0:03:28.87,Default,,0000,0000,0000,,So that's in row 1 column 2.
Dialogue: 0,0:03:28.87,0:03:30.59,Default,,0000,0000,0000,,It's minus 16 plus 6.
Dialogue: 0,0:03:30.59,0:03:31.83,Default,,0000,0000,0000,,And then let's come down here.
Dialogue: 0,0:03:31.83,0:03:33.92,Default,,0000,0000,0000,,So now we're in the\Nsecond row.
Dialogue: 0,0:03:33.92,0:03:35.55,Default,,0000,0000,0000,,So now we're going to use--\Nwe're getting our row
Dialogue: 0,0:03:35.55,0:03:37.93,Default,,0000,0000,0000,,information from the first\Nmatrix-- I know this is
Dialogue: 0,0:03:37.93,0:03:41.38,Default,,0000,0000,0000,,confusing and I feel bad for you\Nright now, but we're going
Dialogue: 0,0:03:41.38,0:03:45.23,Default,,0000,0000,0000,,to a bunch of examples and\NI think it'll make sense.
Dialogue: 0,0:03:45.23,0:03:49.06,Default,,0000,0000,0000,,So this term-- the bottom left\Nterm-- is going to be this row
Dialogue: 0,0:03:49.06,0:03:50.31,Default,,0000,0000,0000,,times this column.
Dialogue: 0,0:03:50.31,0:03:58.01,Default,,0000,0000,0000,,So it's going to be 7 times\N10, so 70, plus 7 times 10
Dialogue: 0,0:03:58.01,0:04:05.65,Default,,0000,0000,0000,,plus 5 times 12, plus 60.
Dialogue: 0,0:04:05.65,0:04:09.29,Default,,0000,0000,0000,,And then the bottom right term\Nis going to be 7 times minus
Dialogue: 0,0:04:09.29,0:04:19.54,Default,,0000,0000,0000,,8, which is minus 56 plus\N5 times minus 2.
Dialogue: 0,0:04:19.54,0:04:22.90,Default,,0000,0000,0000,,So that's minus 10.
Dialogue: 0,0:04:22.90,0:04:31.29,Default,,0000,0000,0000,,So the final product is going to\Nbe 2 times 10 is 20, minus
Dialogue: 0,0:04:31.29,0:04:41.04,Default,,0000,0000,0000,,36, so that's minus 16\Nplus 6, that's 10.
Dialogue: 0,0:04:41.04,0:04:42.22,Default,,0000,0000,0000,,90-- was that what I said?
Dialogue: 0,0:04:42.22,0:04:46.39,Default,,0000,0000,0000,,No, it was-- 70, plus\N60, that's 130.
Dialogue: 0,0:04:46.39,0:04:55.58,Default,,0000,0000,0000,,And then minus 56 minus\N10, so minus 66.
Dialogue: 0,0:04:55.58,0:04:56.40,Default,,0000,0000,0000,,So there you have it.
Dialogue: 0,0:04:56.40,0:04:59.02,Default,,0000,0000,0000,,We just multiplied this matrix\Ntimes this matrix.
Dialogue: 0,0:04:59.02,0:05:00.36,Default,,0000,0000,0000,,Let me do another example.
Dialogue: 0,0:05:00.36,0:05:03.49,Default,,0000,0000,0000,,And I think I'll actually\Nsqueeze it on this side so
Dialogue: 0,0:05:03.49,0:05:06.11,Default,,0000,0000,0000,,that we can write this side out\Na little bit more neatly.
Dialogue: 0,0:05:06.11,0:05:18.63,Default,,0000,0000,0000,,So let's take the matrix and\Nnow 1, 2, 3, 4, times the
Dialogue: 0,0:05:18.63,0:05:27.71,Default,,0000,0000,0000,,matrix 5, 6, 7, 8.
Dialogue: 0,0:05:27.71,0:05:30.20,Default,,0000,0000,0000,,Now we have much more space to\Nwork with so this should come
Dialogue: 0,0:05:30.20,0:05:32.76,Default,,0000,0000,0000,,out neater.
Dialogue: 0,0:05:32.76,0:05:37.46,Default,,0000,0000,0000,,OK, but I'm going to do the\Nsame thing, so to get this
Dialogue: 0,0:05:37.46,0:05:40.35,Default,,0000,0000,0000,,term right here-- the top left\Nterm-- we're going to take--
Dialogue: 0,0:05:40.35,0:05:43.07,Default,,0000,0000,0000,,or the one that has row 1 column\N1-- we're going to take
Dialogue: 0,0:05:43.07,0:05:52.05,Default,,0000,0000,0000,,the row 1 information from\Nhere, and the column 1
Dialogue: 0,0:05:52.05,0:05:54.44,Default,,0000,0000,0000,,information from here.
Dialogue: 0,0:05:54.44,0:05:56.07,Default,,0000,0000,0000,,So you can view it as\Nthis row vector
Dialogue: 0,0:05:56.07,0:05:57.12,Default,,0000,0000,0000,,times this column vector.
Dialogue: 0,0:05:57.12,0:06:01.68,Default,,0000,0000,0000,,So it results, 1 times\N5 plus 2 times 7.
Dialogue: 0,0:06:01.68,0:06:07.73,Default,,0000,0000,0000,,
Dialogue: 0,0:06:07.73,0:06:08.38,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:08.38,0:06:09.61,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:06:09.61,0:06:12.52,Default,,0000,0000,0000,,And so this term, it'll be this\Nrow vector times this
Dialogue: 0,0:06:12.52,0:06:15.74,Default,,0000,0000,0000,,column vector-- let me do that\Nin a different color-- will be
Dialogue: 0,0:06:15.74,0:06:20.55,Default,,0000,0000,0000,,1 times 6 plus 2 times 8.
Dialogue: 0,0:06:20.55,0:06:21.37,Default,,0000,0000,0000,,Let me write that down.
Dialogue: 0,0:06:21.37,0:06:28.59,Default,,0000,0000,0000,,So it's 1 times 6\Nplus 2 times 8.
Dialogue: 0,0:06:28.59,0:06:33.27,Default,,0000,0000,0000,,
Dialogue: 0,0:06:33.27,0:06:34.72,Default,,0000,0000,0000,,Now we go down to\Nthe second row.
Dialogue: 0,0:06:34.72,0:06:38.13,Default,,0000,0000,0000,,And we get our row information\Nfrom the first vector-- let me
Dialogue: 0,0:06:38.13,0:06:44.15,Default,,0000,0000,0000,,circle it with this color--\Nand it is 3 times 5
Dialogue: 0,0:06:44.15,0:06:45.52,Default,,0000,0000,0000,,plus 4 times 7.
Dialogue: 0,0:06:45.52,0:06:52.80,Default,,0000,0000,0000,,
Dialogue: 0,0:06:52.80,0:06:54.76,Default,,0000,0000,0000,,And then we are in the bottom\Nright, so we're in the bottom
Dialogue: 0,0:06:54.76,0:06:57.07,Default,,0000,0000,0000,,row and second column.
Dialogue: 0,0:06:57.07,0:06:59.35,Default,,0000,0000,0000,,So we get our row information\Nfrom here and our column
Dialogue: 0,0:06:59.35,0:07:00.93,Default,,0000,0000,0000,,information from here.
Dialogue: 0,0:07:00.93,0:07:03.86,Default,,0000,0000,0000,,So it's 3 times 6\Nplus 4 times 8.
Dialogue: 0,0:07:03.86,0:07:10.30,Default,,0000,0000,0000,,
Dialogue: 0,0:07:10.30,0:07:13.68,Default,,0000,0000,0000,,And if we simplify,\Nthis is 5 plus--
Dialogue: 0,0:07:13.68,0:07:15.95,Default,,0000,0000,0000,,Well actually, let me just\Nremind you where all the
Dialogue: 0,0:07:15.95,0:07:16.63,Default,,0000,0000,0000,,numbers came from.
Dialogue: 0,0:07:16.63,0:07:18.20,Default,,0000,0000,0000,,So we have that green\Ncolor, right?
Dialogue: 0,0:07:18.20,0:07:25.89,Default,,0000,0000,0000,,This 1 and this 2, that's\Nthis 1 and this 2,
Dialogue: 0,0:07:25.89,0:07:28.62,Default,,0000,0000,0000,,this 1 and this 2.
Dialogue: 0,0:07:28.62,0:07:28.76,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:07:28.76,0:07:30.33,Default,,0000,0000,0000,,And notice, these were in the\Nfirst row and they're in the
Dialogue: 0,0:07:30.33,0:07:31.66,Default,,0000,0000,0000,,first row here.
Dialogue: 0,0:07:31.66,0:07:33.64,Default,,0000,0000,0000,,And this 5 and this 7?
Dialogue: 0,0:07:33.64,0:07:39.92,Default,,0000,0000,0000,,Well, that's this 5 and this\N7, and this 5 and this 7.
Dialogue: 0,0:07:39.92,0:07:42.80,Default,,0000,0000,0000,,So, interesting.
Dialogue: 0,0:07:42.80,0:07:45.41,Default,,0000,0000,0000,,This was in column 1 of the\Nsecond matrix and this is in
Dialogue: 0,0:07:45.41,0:07:47.78,Default,,0000,0000,0000,,column 1 in the product\Nmatrix.
Dialogue: 0,0:07:47.78,0:07:51.03,Default,,0000,0000,0000,,And similarly, the\N6 and the 8.
Dialogue: 0,0:07:51.03,0:07:55.61,Default,,0000,0000,0000,,That's this 6, this 8, and then\Nit's used here, this 6
Dialogue: 0,0:07:55.61,0:07:57.54,Default,,0000,0000,0000,,and this 8.
Dialogue: 0,0:07:57.54,0:08:00.25,Default,,0000,0000,0000,,And then finally this 3 and the\N4 in the brown, so that's
Dialogue: 0,0:08:00.25,0:08:03.98,Default,,0000,0000,0000,,this 3, this 4, and\Nthis 3 and this 4.
Dialogue: 0,0:08:03.98,0:08:05.29,Default,,0000,0000,0000,,And we could of course\Nsimplify all of it.
Dialogue: 0,0:08:05.29,0:08:10.18,Default,,0000,0000,0000,,This was 1 times 5 plus 2 times\N7, so that's 5 plus 14,
Dialogue: 0,0:08:10.18,0:08:15.41,Default,,0000,0000,0000,,so this is 19.
Dialogue: 0,0:08:15.41,0:08:19.20,Default,,0000,0000,0000,,This is 1 times 6 plus 2\Ntimes 8, so it's 6 plus
Dialogue: 0,0:08:19.20,0:08:22.33,Default,,0000,0000,0000,,16, so that's 22.
Dialogue: 0,0:08:22.33,0:08:26.38,Default,,0000,0000,0000,,This is 3 times 5\Nplus 4 times 7.
Dialogue: 0,0:08:26.38,0:08:32.91,Default,,0000,0000,0000,,So 15 plus 28, 38, 43-- if my\Nmath is correct-- and then we
Dialogue: 0,0:08:32.91,0:08:36.25,Default,,0000,0000,0000,,have 3 times 6 plus 4 times 8.
Dialogue: 0,0:08:36.25,0:08:44.22,Default,,0000,0000,0000,,So that's 18 plus\N32, that's 50.
Dialogue: 0,0:08:44.22,0:08:45.98,Default,,0000,0000,0000,,So now let me ask you-- just so\Nyou know that the product
Dialogue: 0,0:08:45.98,0:08:47.69,Default,,0000,0000,0000,,matrix-- just write\Nit neatly-- is
Dialogue: 0,0:08:47.69,0:08:53.61,Default,,0000,0000,0000,,19, 22, 43, and 50.
Dialogue: 0,0:08:53.61,0:08:55.10,Default,,0000,0000,0000,,So now let me ask\Nyou a question.
Dialogue: 0,0:08:55.10,0:08:58.81,Default,,0000,0000,0000,,When we did matrix addition we\Nlearned that if I had two
Dialogue: 0,0:08:58.81,0:09:03.21,Default,,0000,0000,0000,,matrices-- it didn't matter what\Norder we added them in.
Dialogue: 0,0:09:03.21,0:09:06.97,Default,,0000,0000,0000,,So if we said, A plus B-- and\Nthese are matrices; that's why
Dialogue: 0,0:09:06.97,0:09:09.34,Default,,0000,0000,0000,,I'm making them all bold-- we\Nsaid this is the same thing as
Dialogue: 0,0:09:09.34,0:09:12.33,Default,,0000,0000,0000,,B plus A, based on how\Nwe define matrix
Dialogue: 0,0:09:12.33,0:09:15.52,Default,,0000,0000,0000,,addition, B plus A.
Dialogue: 0,0:09:15.52,0:09:17.06,Default,,0000,0000,0000,,So now let me ask\Nyou a question.
Dialogue: 0,0:09:17.06,0:09:22.97,Default,,0000,0000,0000,,Is multiplying two matrices,\Nis AB-- that's just means
Dialogue: 0,0:09:22.97,0:09:26.46,Default,,0000,0000,0000,,we're multiplying A and B-- is\Nthat the same thing as BA?
Dialogue: 0,0:09:26.46,0:09:30.09,Default,,0000,0000,0000,,
Dialogue: 0,0:09:30.09,0:09:30.82,Default,,0000,0000,0000,,Does it matter?
Dialogue: 0,0:09:30.82,0:09:33.80,Default,,0000,0000,0000,,Does the order of the matrix\Nmultiplication matter?
Dialogue: 0,0:09:33.80,0:09:36.31,Default,,0000,0000,0000,,And so, I'll tell you right\Nnow, it actually matters a
Dialogue: 0,0:09:36.31,0:09:37.09,Default,,0000,0000,0000,,tremendous amount.
Dialogue: 0,0:09:37.09,0:09:39.55,Default,,0000,0000,0000,,And actually there are certain\Nmatrices that you can add in
Dialogue: 0,0:09:39.55,0:09:42.04,Default,,0000,0000,0000,,one direction that you can't\Nadd in the other-- oh, that
Dialogue: 0,0:09:42.04,0:09:47.30,Default,,0000,0000,0000,,you can multiply in one way but\Nyou can't multiply in the
Dialogue: 0,0:09:47.30,0:09:48.20,Default,,0000,0000,0000,,other order.
Dialogue: 0,0:09:48.20,0:09:50.76,Default,,0000,0000,0000,,And well, I'll show you that\Nin an example-- but just to
Dialogue: 0,0:09:50.76,0:09:52.80,Default,,0000,0000,0000,,show that this isn't even equal\Nfor most matrices, I
Dialogue: 0,0:09:52.80,0:09:56.64,Default,,0000,0000,0000,,encourage you to multiply these\Ntwo matrices in the
Dialogue: 0,0:09:56.64,0:09:57.11,Default,,0000,0000,0000,,other order.
Dialogue: 0,0:09:57.11,0:09:58.95,Default,,0000,0000,0000,,Actually let me do that.
Dialogue: 0,0:09:58.95,0:10:00.63,Default,,0000,0000,0000,,Let me do that really\Nfast just to prove
Dialogue: 0,0:10:00.63,0:10:01.44,Default,,0000,0000,0000,,the point to you.
Dialogue: 0,0:10:01.44,0:10:02.83,Default,,0000,0000,0000,,So let me delete all\Nthis top part.
Dialogue: 0,0:10:02.83,0:10:06.04,Default,,0000,0000,0000,,
Dialogue: 0,0:10:06.04,0:10:13.83,Default,,0000,0000,0000,,Let me delete all of it, and\Nactually I can delete to this.
Dialogue: 0,0:10:13.83,0:10:15.96,Default,,0000,0000,0000,,So hopefully, you know that when\NI multiply this matrix
Dialogue: 0,0:10:15.96,0:10:17.85,Default,,0000,0000,0000,,times this matrix, I got this.
Dialogue: 0,0:10:17.85,0:10:20.25,Default,,0000,0000,0000,,So let me switch the order--\Nand I'll do it fairly fast
Dialogue: 0,0:10:20.25,0:10:23.14,Default,,0000,0000,0000,,just so as to not bore you-- so\Nlet me switch the order of
Dialogue: 0,0:10:23.14,0:10:24.15,Default,,0000,0000,0000,,the matrix multiplication.
Dialogue: 0,0:10:24.15,0:10:26.76,Default,,0000,0000,0000,,This is good as this is another\Nexample-- so I'm going
Dialogue: 0,0:10:26.76,0:10:36.74,Default,,0000,0000,0000,,to multiply this matrix: 5, 6,\N7, 8, times this matrix-- and
Dialogue: 0,0:10:36.74,0:10:40.40,Default,,0000,0000,0000,,I just switched the order; and\Nwe're testing to see whether
Dialogue: 0,0:10:40.40,0:10:46.70,Default,,0000,0000,0000,,order matters-- 1, 2, 3, 4.
Dialogue: 0,0:10:46.70,0:10:49.01,Default,,0000,0000,0000,,Let's do it-- and I won't do all\Nthe colors and everything,
Dialogue: 0,0:10:49.01,0:10:49.69,Default,,0000,0000,0000,,I'll just do it systematically.
Dialogue: 0,0:10:49.69,0:10:54.33,Default,,0000,0000,0000,,I think you just have to see a\Nlot of examples here-- So this
Dialogue: 0,0:10:54.33,0:10:56.41,Default,,0000,0000,0000,,first term gets its row\Ninformation from the first
Dialogue: 0,0:10:56.41,0:10:58.81,Default,,0000,0000,0000,,matrix, column information\Nfrom the second matrix.
Dialogue: 0,0:10:58.81,0:11:06.34,Default,,0000,0000,0000,,So it's 5 times 1 plus 6 times\N3, so it's 5 times 1--
Dialogue: 0,0:11:06.34,0:11:09.13,Default,,0000,0000,0000,,Let me just write,\Nactually edit.
Dialogue: 0,0:11:09.13,0:11:17.65,Default,,0000,0000,0000,,I'm going to skip a step here--\NOK so it's 5 times 1
Dialogue: 0,0:11:17.65,0:11:23.48,Default,,0000,0000,0000,,plus 6 times 3, plus 18.
Dialogue: 0,0:11:23.48,0:11:25.11,Default,,0000,0000,0000,,What's the second term here?
Dialogue: 0,0:11:25.11,0:11:29.65,Default,,0000,0000,0000,,It's going to be 5 times\N2 plus 6 times 4.
Dialogue: 0,0:11:29.65,0:11:40.19,Default,,0000,0000,0000,,So 5 times 2 is 10, plus\N6 times 4 is 24.
Dialogue: 0,0:11:40.19,0:11:42.39,Default,,0000,0000,0000,,Right, now we just took\Nthis row times this
Dialogue: 0,0:11:42.39,0:11:44.68,Default,,0000,0000,0000,,column right here.
Dialogue: 0,0:11:44.68,0:11:48.03,Default,,0000,0000,0000,,OK now we're down here for the\Nset-- so then we're doing this
Dialogue: 0,0:11:48.03,0:11:51.10,Default,,0000,0000,0000,,row, this element right here at\Nthe bottom left is going to
Dialogue: 0,0:11:51.10,0:11:52.96,Default,,0000,0000,0000,,use this row, and this column.
Dialogue: 0,0:11:52.96,0:12:00.41,Default,,0000,0000,0000,,So it's 7 times 1\Nplus 8 times 3.
Dialogue: 0,0:12:00.41,0:12:02.98,Default,,0000,0000,0000,,8 times 3 is 24.
Dialogue: 0,0:12:02.98,0:12:05.43,Default,,0000,0000,0000,,And then finally, to get this\Nelement we're essentially
Dialogue: 0,0:12:05.43,0:12:11.82,Default,,0000,0000,0000,,multiplying this row times this\Ncolumn, so it's 7 times 2
Dialogue: 0,0:12:11.82,0:12:21.81,Default,,0000,0000,0000,,is 14, plus 8 times\N4, plus 32.
Dialogue: 0,0:12:21.81,0:12:30.02,Default,,0000,0000,0000,,So this is equal to 5\Nplus 18 is 23, 34.
Dialogue: 0,0:12:30.02,0:12:31.10,Default,,0000,0000,0000,,What's 7 plus 24?
Dialogue: 0,0:12:31.10,0:12:35.53,Default,,0000,0000,0000,,That's 31, 46.
Dialogue: 0,0:12:35.53,0:12:44.14,Default,,0000,0000,0000,,So notice, if we called\Nthis matrix A and this
Dialogue: 0,0:12:44.14,0:12:47.08,Default,,0000,0000,0000,,is matrix B, right?
Dialogue: 0,0:12:47.08,0:12:57.56,Default,,0000,0000,0000,,In the last example, we showed\Nthat A times B is equal to 19,
Dialogue: 0,0:12:57.56,0:13:02.64,Default,,0000,0000,0000,,22, 43, 50.
Dialogue: 0,0:13:02.64,0:13:06.55,Default,,0000,0000,0000,,And we just showed that, well,\Nif you reverse the order, B
Dialogue: 0,0:13:06.55,0:13:10.22,Default,,0000,0000,0000,,times A is actually this\Ncompletely different matrix.
Dialogue: 0,0:13:10.22,0:13:12.23,Default,,0000,0000,0000,,So the order in which\Nyou multiply
Dialogue: 0,0:13:12.23,0:13:15.14,Default,,0000,0000,0000,,matrices completely matters.
Dialogue: 0,0:13:15.14,0:13:16.33,Default,,0000,0000,0000,,So I'm actually running\Nout of time.
Dialogue: 0,0:13:16.33,0:13:19.21,Default,,0000,0000,0000,,In the next video I going talk\Na little bit more about the
Dialogue: 0,0:13:19.21,0:13:22.26,Default,,0000,0000,0000,,types of matrix-- well, one, we\Nknow that order matters--
Dialogue: 0,0:13:22.26,0:13:25.11,Default,,0000,0000,0000,,and in the next video I'll\Nshow that what type of
Dialogue: 0,0:13:25.11,0:13:27.46,Default,,0000,0000,0000,,matrices can be multiplied\Nby each other.
Dialogue: 0,0:13:27.46,0:13:29.82,Default,,0000,0000,0000,,When we added or subtracted\Nmatrices, we just said, well
Dialogue: 0,0:13:29.82,0:13:31.85,Default,,0000,0000,0000,,they have to have the same\Ndimensions because you're
Dialogue: 0,0:13:31.85,0:13:33.86,Default,,0000,0000,0000,,adding or subtracting\Ncorresponding terms. But
Dialogue: 0,0:13:33.86,0:13:37.04,Default,,0000,0000,0000,,you'll see with multiplication\Nit's a little bit different.
Dialogue: 0,0:13:37.04,0:13:38.25,Default,,0000,0000,0000,,And we'll do that in\Nthe next video.
Dialogue: 0,0:13:38.25,0:13:39.79,Default,,0000,0000,0000,,See you soon.
Dialogue: 0,0:13:39.79,0:13:39.90,Default,,0000,0000,0000,,