SOLUTION: if P = {{{(matrix(2,3,2,-1,4,-1,3,0))}}} and Q = {{{(matrix(3,2,3,2,1,1,-2,0))}}} evaluate PQ

Algebra ->  Test -> SOLUTION: if P = {{{(matrix(2,3,2,-1,4,-1,3,0))}}} and Q = {{{(matrix(3,2,3,2,1,1,-2,0))}}} evaluate PQ      Log On


   

Question 117532: if P = %28matrix%282%2C3%2C2%2C-1%2C4%2C-1%2C3%2C0%29%29 and
Q = %28matrix%283%2C2%2C3%2C2%2C1%2C1%2C-2%2C0%29%29
evaluate PQ
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
if P = %28matrix%282%2C3%2C2%2C-1%2C4%2C-1%2C3%2C0%29%29 and
Q = %28matrix%283%2C2%2C3%2C2%2C1%2C1%2C-2%2C0%29%29
evaluate PQ
    
PQ = %28matrix%282%2C3%2C2%2C-1%2C4%2C-1%2C3%2C0%29%29·%28matrix%283%2C2%2C3%2C2%2C1%2C1%2C-2%2C0%29%29

Since the first matrix is 2×3 and the second matrix is 3×2, 

the fact that the "inner" dimensions are both the same, 3, the
matrices can be multiplied, and the result will be a matrix
whose dimensions are the "outer" dimensions of those, 2×2.

So the product is

%28matrix%282%2C3%2C2%2C-1%2C4%2C-1%2C3%2C0%29%29·%28matrix%283%2C2%2C3%2C2%2C1%2C1%2C-2%2C0%29%29 =  = %28matrix%282%2C2%2C-3%2C3%2C0%2C1%29%29

Edwin