Can Matrices AB, BA, CD, and DC be Evaluated?

[Buster617]

Homework Statement

Hi all. I am doing this work and can't seem to find any information on this in any of my notes or textbooks. The question is, "Evaluate (if possible) AB, BA, CD and DC", this is what i need some help with.
I also have further on the question, "Evaluate | u |, | v |, u . v and u * v", but this one i can do already so i don't need help with this one.

I know that a single matrix can't be evaluated exactly and since i can't find anything on evaluating either a single matrix or multiple matrices, i assume at the moment that, it is not possible to evaluate these from the first question either?

The relevant equations are below:

$$A = \left(\begin{array}{c} 21 \ 60 & 2 \ 7 \end{array}\right)$$
$$B = \left(\begin{array}{c} 4 \ -5 & 3 \ -2 \end{array}\right)$$
$$C = \left(\begin{array}{c} 15 \ 3 \ 7 & 5 \ 12 \ 4 \end{array}\right)$$
$$D = \left(\begin{array}{c} 3 \ 5 \ 15 & 1 \ -1 \ 7 & -5 \ 1 \ 8 \end{array}\right)$$Any help/ information would be greatly appreciated. Thanks

 

[HallsofIvy]

You seem to be having a problem with the word "evaluate". You certainly can evaluate a single matrix- its value is itself. Similarly, "evaluating" AB simply means finding the product of matrices A and B. AB, CD, and DC also mean just "multiply the matrices".

 

[Buster617]

Ahh ok, i get it now. Thanks a lot.
Just done them all and they seem correct, I've still come up with DC not being possible due to there being a different number of columns in the first matrix compared to the number of rows in the second matrix.

Thanks again

 

[HallsofIvy]

Yes, that is correct. DC is not a possible multiplication. (But CD is.)