Sample Question #143 (applied math – matrices)

Assume two matrices *A *and *B *have the appropriate dimensions and "nice" properties (e.g., conformable), so you need not worry about the validity of the calculations. Is each of the following true or false? If false, what’s the correct relationship?

- (
*AB*)^{T}=*A*^{T}*B*^{T} *AB = BA**A*kr.*B*<>*B*kr.*A*, where kr. stands for Kronecker product and <> means not equal to- tr(
*A+B*) = tr(*A*) + tr(*B*) + 2 * tr(*AB*)

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ANSWER

1. False. Should be B’A’ (where ‘ is another way of denoting transpose)

2. False. Should be unequal; no general relationship exists

3. True.

4. False. Drop the last term on the right. (BTW, you should have known that tr stands for trace.)