# Distribution of linear combinations multivariate normal

Suppose $Y$ ~ $N_{3}(\mu,\sum)$

Let $\mu= \begin{bmatrix} 1 \\ 4 \\ 8 \end{bmatrix}$ and $\sum= \begin{bmatrix} 1 & 1 & 1 \\ 1 & 8 & 2 \\ 1 & 2 & 6 \end{bmatrix}$

Let $X=3Y_{1}-4Y_{2}+Y_{3}$

What is the distribution of $X$? I know it reduces to a scalar but I am not quite sure exactly how to compute the matrix operations to get there.