Given the following matrices find E times F

Question

E=[0 1]     F=[1 2 0]
    [-1 2]        [-1 -2 -1]
    [1 3]
(All of the brackets for each E and F should actually be conjoined)
First row=? second row=? third row=?

Answer 1

E is a 3 x 2 matrix  and F is a 2 x 3 matrix.  Since the number of columns in matrix E equals the number of rows in matrix F, we can perform cross multiplication.  Our matrix product will be a 3 x 3 matrix.

 

We multiply the each element in the rows of the 1st matrix by each element in the columns of the 2nd matrix.  Then add the products.

 

0(1) + 1(-1)     0(2) + 1(-2)     0(0) + 1(-1)

 

-1(1) + 2(-1)     -1(2) + 2(-2)     -1(0) + 2(-1)

 

1(1) + 3(-1)       1(2) + 3(-2)       1(0) + 3(-1)

 

 

      becomes

 

-1   -2   -1

 

-3   -6     -2

 

-2    -4    -3