matrices: A=[-5 4 -6
9 -8 7
4 -3 9]
B=[-2 4 -5
8 9 3
5 -2 2]
AB=?
please show work if you can.
To find the product AB, we need to multiply each element of matrix A with the corresponding element of matrix B, and then sum up the products.
The product of two matrices A and B is denoted as AB, where the number of columns of A is equal to the number of rows of B. In our case, matrix A is a 3x3 matrix and matrix B is also a 3x3 matrix, so we can proceed with the multiplication.
First, let's find the element in the first row and first column of the resulting matrix AB. To do this, we multiply the corresponding elements of the first row of matrix A with the corresponding elements of the first column of matrix B, and sum up the products.
For the first element of AB:
A[1,1] * B[1,1] + A[1,2] * B[2,1] + A[1,3] * B[3,1]
= (-5) * (-2) + 4 * 8 + (-6) * 5
= 10 + 32 - 30
= 12
Now, let's find the element in the first row and second column of AB:
A[1,1] * B[1,2] + A[1,2] * B[2,2] + A[1,3] * B[3,2]
= (-5) * 4 + 4 * 9 + (-6) * (-2)
= -20 + 36 + 12
= 28
We repeat this process for every element in the resulting matrix AB.
The resulting matrix AB is given by:
AB = [12 28 -19
93 125 18
25 50 -11]
Therefore, the product AB is:
AB = [12 28 -19
93 125 18
25 50 -11]