00:01
In this question, given the matrices a and b, we are asked to calculate a b and b if they are defined.
00:08
So first let's try to calculate the product ab.
00:22
To multiply the matrix a by the matrix b, we need to multiply the first row of a by each of the columns of the matrix b.
00:34
To get the first row of the matrix a -b, to multiply the first row of the matrix a by the first column of the matrix b, we need to multiply their entries and then add them up.
00:50
We are going to get 3 times negative 1 plus 4 times 5.
00:56
And that's going to be the entry in the position 1 -1.
01:01
The next entry is going to be 3 times 0 plus 4 times negative 2.
01:07
The last entry is going to be 3 times 4 plus 4 times 3.
01:16
Now, to get the second row, we will multiply the second row with the matrix 8 by each of the columns of the matrix b.
01:29
We are going to get 3 times negative 1 plus 4 times 5, 3 times 0 plus 4 times negative 2, 3 times 4 plus 4 times 3.
01:46
So basically it's going to be same as the first row because, well, the rows of the matrix a are same.
01:57
And we are going to get negative 3 plus 20 is 17...