Question

A has a rows and a+3 columns B has b rows and 17-b columns and if both products AB and BA exist find a b?​

Answer 1

Answer:

a=7 and b=10

Step-by-step explanation:

A is an a×(a+3) matrix and B is a b×(17-b) matrix.

We know that the product of two matrices A(m×n) and B(p×q) is possible only when n=p and the dimensions of the product matrix AB will be (m×p).

So, for AB to exist, a+3=b, ⇒a-b=-3 ...... (1)

Again, for BA to exist, 17-b=a, ⇒a+b=17 ...... (2)

Solving equations (1) and (2), we get, 2a=14, ⇒a=7.

And from equation (2), b=(17-a)=(17-7)=10

Therefore, a=7 and b=10. (Answer)