if A and B are 7 x 6 matrices and C is a 4 x 7 matrix which

if A and B are 7 x 6 matrices, and C is a 4 x 7 matrix, which of the following are defined?

A) B-C

B) AB^T

C) A+B

D) C^T

E) AC

F) CA

Solution

A) B is 7x6 and C is 4x7 Hence B-C is not defined

B) B^T = 6x7 and A = 7x6

Hence AB^T is defined and result will be 7x7 matrix

c) A+B is well defined as both are of the same order

d) c^T is well defined and is a 7x4 matrix.

e) AC cannot be done as no of columns of A not equals no of rows of C

f) CA is well defined as no of columns of C equals no of rows of A and result is a 4x6 matrix.