Question 627191: Find the given element of the matrix product C = AB.
A=
[4,2,-1,0]
[5,-5,0,3]
[-1,3,4,1]
B=
[4,-1,1]
[1,1,0]
[-3,0,5]
[0,-5,2]
C23=
Answer by hammy(9)   (Show Source):
You can put this solution on YOUR website! When you multiply matrices, you take the first row and multiply every single element in that row with every corresponding element in the other column. Then, you take the sum of the products of the corresponding elements and that will be the element of the first row of the first column of the resulting matrix. You must do the same with the same first row and the next column and so on. Once you run out of columns, use the second row and the same columns. For example,
[a b c d] * [1]
[2]
[3]
[4]
Thusly, the resulting matrix will be [a+2b+3c+4d]
As you can see, that is a 1x1 matrix since the order of the two matrices was 1x4 and 4x1. The resulting matrix's order will always be the number of rows of the first matrix x number of columns of the second matrix
However, the order must always be like this: a x b and b x a.
So,
[4,2,-1,0]
[5,-5,0,3] *
[1,1,0]
[4,-1,1]
[1,1,0]
[-3,0,5]
[0,-5,2] = [21 -2-1]
[15 -25 11]
We don't need the third row because the problem only asks for the element in the second row and the third column. In this case, the element is 11
So, c23=11
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