Determine whether the product AB is defined, indicate what the dimensions of the product matrix will be, and find the product matrix, given

The product AB is defined:

the product matrix will be 2 × 2. Matrix multiplication is then accomplished by a simple series of row-column vector multiplications to determine the various elements of the product matrix. The a11 element of the product matrix is determined by the product of the first row R1 of the lead matrix and the first column C1 of the lag matrix; the a12 element of the product matrix is determined by the product of the first row R1 of the lead matrix and the second column C2 of the lag matrix. In general, the aij element of the product matrix is determined by the product of the ith row Ri of the lead matrix and the jth column Cj of the lag matrix. Thus

Transcribed Image Text:

8 5 2 7 A = B = 6 3 41