Random vectors & random matrices (1)

1) Theorem: **E**(**X**+**Y**)=**E**(**X**)+**E**(**Y**)

where X and Y are random (matrices? vectors?).

The source didn't specify the nature of **X** and **Y**. Can **X** and **Y** be random __matrices__ of __any__ dimension (provided **X**+**Y** is defined, of course), or must **X** and **Y** be random __vectors__?

2) Let A be a constant matrix (i.e. all elements are fixed (nonrandom)). Can we now use the **E**(**X**+**Y**)=**E**(**X**)+**E**(**Y**) with **Y**=**A** to show that

**E**(**X**+**A**) = **E**(**X**)+**E**(**A**) = **E**(**X**)+**A **?

My main question here is: can we treat **A** as a special case of a __RANDOM__ matrix even though A is __not__ random, and use the above theorem which requires both **X** and **Y** be random?

A similar question: if X constantly takes on the value 5, a lot of times we will say that X is nonrandom, but can X here be treated as a random variable?

Thanks!

note: also under discussion in Talk Stats forum