Question 1058404: If A and B are 3×6 matrices, and CC is a 9×3 matrix, which of the following are defined?
A. A+C
B. CA
C. BC
D. B-A
E. CB-A
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I think instead of CC, you just meant to write C.
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A+C is NOT defined since A is a 3x6 matrix while C is a 9x3 matrix. The dimensions don't match up. Both rows and columns must be the same value (eg: both need to be 3x6 matrices) for it to work.
CA is defined because C is 9x3 while A is 3x6. The inner dimensions, both "3", match up. So multiplication is allowed here.
BC is NOT defined because B is 3x6 while C is 9x3. The inner dimensions of 6 and 9 do NOT match up.
B-A is defined because both A and B are the same size: 3x6
CB is defined for similar reasons that CA is defined. CB is going to be a 9x6 matrix while A is a 3x6 matrix. The dimensions don't match up. So CB-A is NOT defined.
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To summarize, the following answers are
CA
B-A
Everything else is undefined.
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