It A B and C are 3 times 3 3 times 7 and 7 times 9 matrices

It A, B, and C are 3 times 3, 3 times 7, and 7 times 9 matrices respectively, determine which of the following products are defir For those defined, enter the size of the resulting matrix (e.g. \"3 times 4\", with spaces between numbers and \"x\"). For those undefined enter \'undefined\'. CB: BC: BA: A^2:

Solution

A : 3 x 3

B : 3 x 7

C : 7 x 9

for AB to exist (that is, for the very process of matrix multiplication to be able to function sensibly), A must have the same number of columns as B has rows; looking at the matrices, the rows of A must be the same length as the columns of B.

i) CB ( 7 x 9) : ( 3 x 7 ) =Product does not exist

ii) BC ( 3 x 7) : ( 7 x 9) Resulting matrix 3 x 9

iii) BA (3 x 7) : (3 x 3 ) Product does not exist

iv ) A^2 ( 3 x 3 ) : (3 x 3) Resulting matrix 3 x 3