Why isLet $\displaystyle X$ and $\displaystyle Y$ be random variables and $\displaystyle a,b,c,d \in \mathbb{R}$. When is

$\displaystyle Z=\left[ \begin{matrix}a & b \\ c & d \end{matrix} \right]\left[ \begin{matrix}X \\ Y\end{matrix} \right]$

a multivariate random variable?

- when $\displaystyle aX+bY\neq cX+dY$
- always
- when $\displaystyle ad-bc\neq 0$
- when $\displaystyle aX+bY=cX+dY$
- never
- when $\displaystyle ad-bc=1$
2ndanswer the right one? Just because $\displaystyle Z=\left[ \begin{matrix}aX+bY \\ cX+dY \end{matrix} \right]$ is always a "well defined" (I'm making the terminology up) and, after all, that is the definition of a multivariate random variable (Wikipedia doesn't give one, though)?