Subject: Matrices "conformable"

Name: Wayne

Who is asking: Parent
Level: Secondary

Question:
Can someone explain the concept of conformable matrices in a way that is easy to understand ? One definition says to multiply matrices rows and columns must conform, ie, 5 x 3 matrix times a 3 x 5 matrix. In the next example, however a 8 x 1 matrix and a 8 x 3 matrix are said to be conformable ! Help !

It looks to me like "conformable" in this context could only mean that multiplication is possible - i.e. if A is n x k and B is k x m, then the product AB makes sense and so A and B are "comformable for multiplication (in that order)". Hence for your example if A is a 5 x 3 matrix and B is a 3 x 5 matrix then AB and BA are both possible so they are conformable for multiplication in both orders.

As for you example that an 8 x 3 and 8 x 1 are said to conformable, I'm baffled. Could there be an error in his text? Possibly it's a typo of "8 x 8 and 8 x 1" or "1 x 8 and 8 x 3". Do you know what source the asker had for this definition ?