If A and B are 8 x2 matrices, and C is a 5 x 8 matrix, which of the following are defined?

Question

If A and B are 8 x2 matrices, and C is a 5 x 8 matrix, which of the following are defined?

A. B–A
B. AC
C. C transpose
D. BA transpose
E. CB
F. C+A

Answer 1

A. since B and A have the same dimensions, B - A is defined.
B. since A is 8x2, AX is defined only if X is a 2xn matrix.
C. transpose is always defined
D. B(A transpose) is 8x2 times 2x8, which is defined
E. CB is 5x8 times 8x2, defined, resulting in a 5x2 matrix.
F. not defined since not same dimensions.

Answer 2

A. since B and A have the same dimensions, B - A is possible and defined.
B. since A is 8x2,and C is 5x8 it is not defined( because for a matrix to be able to mutiply another both of them sholuld have their orders in the form as mxn and nxp ).
C. transpose is defined for any kind of matrix
D. (BA) transpose is not defined) but B(A transpose) is defined
E. CB is defined and is a 5x2 matrix.
F. A+B isnot defined since not same dimensions.

Answer 3

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