1. The problem involves multiplying a 3x3 matrix: $$\begin{bmatrix}-60 & -12 & 144 \\ -442 & -234 & -104 \\ -180 & -260 & 240\end{bmatrix}$$ by a 3x1 column vector: $$\begin{bmatrix}5c \\ y \\ z\end{bmatrix}$$ 2. Matrix multiplication is performed by taking the dot product of each row of the matrix with the column vector. 3. The first element of the product is: $$ (-60)(5c) + (-12)(y) + 144(z) = -300c - 12y + 144z $$ 4. The second element is: $$ (-442)(5c) + (-234)(y) + (-104)(z) = -2210c - 234y - 104z $$ 5. The third element is: $$ (-180)(5c) + (-260)(y) + 240(z) = -900c - 260y + 240z $$ 6. Therefore, the resulting vector is: $$\begin{bmatrix}-300c - 12y + 144z \\ -2210c - 234y - 104z \\ -900c - 260y + 240z\end{bmatrix}$$ This is the final answer after performing the matrix-vector multiplication.