0:02 in this video we're going to focus on a
0:06 scalar multiplication of matrices so
0:06 so
0:09 let's begin with matrix a let's say it's 5
0:10 5
0:11 negative 2
0:13 7 3
0:15 and matrix b
0:18 we're going to say it's negative 4 6
0:21 negative 2 and 9.
0:23 now let's find the values of 3a
0:24 3a
0:27 and 4b
0:29 so 3a all we need to do is multiply
0:30 matrix a
0:32 by three
0:34 so every element in this matrix
0:36 we're gonna multiply it by three
0:38 so three times five is fifteen
0:41 three times negative two is negative six
0:43 three times seven is twenty-one
0:46 3 times 3 is 9. and that's it
0:49 so for 4b it's just going to be 4 times
0:55 so 4 times negative 4
0:58 that's negative 16. four times six is twenty-four
1:00 twenty-four
1:01 four times negative two is negative
1:05 eight four times nine is thirty-six and
1:06 and
1:09 that's scalar multiplication
1:10 now you also need to be familiar with
1:14 operations uh associated with matrices
1:16 that involve scalar multiplication and
1:18 we're going to go over some examples
1:26 now let's say if we want to find the
1:28 value of 5a
1:33 how can we do that so we got to multiply
1:35 matrix a
1:39 and then there's going to be a
1:41 subtraction sign and then we're going to
1:43 multiply matrix b
1:45 by 6
1:47 or negative 6.
1:49 if you multiply by 6 the negative sign
1:52 will remain here but if you multiply by
1:53 negative 6
1:55 you could change it and put a plus sign
1:57 which i think it's easier
1:59 so first let's multiply this matrix by five
2:01 five
2:03 so five times five is twenty-five
2:07 five times negative two is negative ten
2:09 times 7 is 35
2:12 5 times 3 is 15.
2:14 and then let's put a plus sign and
2:16 multiply everything in this matrix by
2:19 negative 6.
2:21 so negative 6 times negative 4 is
2:22 positive 24
2:25 negative 6 times 6 is
2:26 negative 36
2:29 negative 6 times negative 2 is 12
2:31 and negative 6 times 9 that's going to
2:37 so now
2:40 all we need to do
2:42 is add the two matrices
2:44 and this will give us the value of 5a
2:51 so let's add the elements in the first
2:54 row and in the first column
2:56 25 plus 24
2:58 that's 49
3:00 and then let's add the elements in the
3:02 first row second column
3:05 negative 10 plus negative 36
3:08 is negative 46.
3:09 now let's move on to
3:12 second row first column
3:15 35 plus 12
3:17 is 47
3:19 and then finally
3:21 the second rule second column 15
3:24 15
3:27 plus negative 54
3:29 is negative 39
3:33 and so that's it for this problem
3:35 now let's try another example let's say
3:36 we have
3:37 matrix c
3:39 and it has the numbers 4
3:41 6 negative 2
3:43 3 7 8
3:45 8
3:51 five negative two three
3:52 negative seven
3:59 so go ahead and perform this operation
4:03 find a matrix that corresponds to 3c
4:19 and then plus seven
4:20 seven
4:27 feel free to pause the video if you want
4:30 to work on this example
4:32 so let's multiply element c i mean
4:35 matrix c by three
4:38 three times four is twelve three times
4:40 six is eighteen
4:41 and then three times negative 2 that's
4:42 negative 6
4:44 and then we're going to have 9 21
4:46 21
4:49 and 24.
4:51 and then let's multiply every element in
4:52 matrix d
4:53 by 7.
4:56 so 7 times 5 is 35
5:00 7 times negative 2 that's negative 14.
5:02 7 times 3 is 21
5:05 7 times negative 7
5:09 is negative 49 and then we'll have 28
5:16 now let's add
5:18 the two matrices
5:28 so first let's add 12 and 35
5:31 12 plus 35 is 47
5:33 and then let's add 18
5:37 and negative 14 which will give us 4
5:40 and then negative 6 plus 21
5:46 and then
5:48 we have 9 and negative 49
5:52 which is negative 40.
5:54 21 plus 28
5:57 that's 49
6:01 and then 24 plus negative 63
6:03 or 24 minus 63
6:05 that's going to be negative
6:06 negative 39
6:08 39
6:10 and that's it so now you know how to
6:14 perform operations with matrices
