00:01
In part a, we determine 2a minus 3b.
00:04
And so this equals 2 times of a matrix.
00:08
We replace a matrix that is 1 negative 2, 0 negative 1 minus 3 times of b matrix, which is 3 .0 negative 1.
00:21
And so here we multiply this a matrix by 2.
00:27
That is we multiply each of the elements in a matrix by 2.
00:31
So 1 times 2 is 2.
00:34
Negative 2 times 2 is negative 4.
00:37
0 times 2 is 0.
00:40
And then negative 1 times 2 is negative 2.
00:45
And here we multiply each of the elements in b matrix by negative 3.
00:50
So i write down this as plus 3 times negative 3 is negative 9.
00:56
0 times negative 3 is 0 and negative 1 times negative 3 is positive 3 and then 2 times negative 3 is negative 6.
01:07
We now perform addition of these two matrices by adding the corresponding elements.
01:13
So we add 2 negative 9 which is negative 7 and then negative 4 plus 0 is negative 4.
01:21
0 plus 3 is 3 and then negative 2, negative 6 is negative 2.
01:26
8 and so this is the result of the matrix 2a minus 3b in part b we determine minus 3a plus b and so this equals negative 3 times of the a matrix replace a matrix that is 1 negative 2 0 negative 1 we then put plus b matrix that is 3 0 negative 1 2 and now we should multiply each of the a matrix with negative 3.
02:04
So 1 times negative 3 is negative 3.
02:07
Negative 2 times negative 3 is positive 6 and 0 0.
02:13
Negative 1 times negative 3 is positive 3.
02:17
This must be added with the b matrix that is 3 negative 1 2.
02:23
We now add the corresponding elements to perform this addition.
02:28
It is negative 3 plus 3 is 0 6 plus 0.
02:33
Is 6.
02:34
0, negative 1 is negative 1.
02:38
And then 3 plus 2 is 5.
02:41
And so this is the result of the matrix, negative 3a plus b.
02:48
In part c, we determine the multiplication of the matrices a and b in the order ab.
02:55
And first we have to determine if matrix multiplication is possible.
03:00
For that, we determine the order of this matrix.
03:04
The order of matrix, the order of matrix is.
03:05
A is two rows and two columns and the order of matrix b is two rows and two columns.
03:12
That is basically these two matrices or square matrices.
03:16
So therefore matrix multiplication is possible in any order.
03:21
So let's determine this multiplication of matrix a with b in the order ab.
03:26
So first i write down the matrix a, that is 1 negative 2, 0, negative 1.
03:32
Now i put the second matrix that is 3 -0 negative 1, 2.
03:39
Let's perform this multiplication as like this.
03:43
That is first we consider the first row element of matrix a, multiply them with the first column elements of matrix b.
03:52
That is 1 should be multiplied with 3.
03:55
We put 1 multiplied with 3.
03:57
And then we have to sum this with the multiplication of these elements, that is negative 2, negative 1.
04:05
So i write negative 2 times negative 1.
04:07
We have now completed for the first column.
04:11
We now move on to the next column in the b matrix.
04:14
So once again we perform the corresponding elements.
04:17
That is 1 multiplied with 0 plus negative 2 multiplied with 2.
04:25
And this we have performed for the first row elements of the result matrix.
04:30
So we put this in matrix form.
04:36
Now we consider the second row element of matrix a, multiply with the first column elements of matrix b.
04:44
That is 0 multiplied with 3.
04:47
Right on 0 multiplied with 3...