Let ([X, Y]^{top}) be uniformly distributed on the triangle with corners ((0,0),(1,2)), and ((-1,1)). Give the distribution

Question:

Let $[X, Y]^{\top}$ be uniformly distributed on the triangle with corners $(0,0),(1,2)$, and $(-1,1)$. Give the distribution of $[U, V]^{\top}$ defined by the linear transformation

\[ \left[\begin{array}{l} U \\ V \end{array}\right]=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right]\left[\begin{array}{l} X \\ Y \end{array}\right] \]

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