Let $$\vec{v}_1=\left[\begin{array}{c} 0\cr -3\cr 3 \end{array}\right], \vec{v}_2 = \left[\begin{array}{c} 2\cr 3\cr 0 \end{array}\right], \vec{v}_3 = \left[\begin{array}{c} -3\cr 0\cr 2 \end{array}\right]$$ be eigenvectors of the matrix $A$ which correspond to the eigenvalues $\lambda_1 = -2$, $\lambda_2 = -1$, and $\lambda_3 = 2$, respectively, and let $$\vec{x}=\left[\begin{array}{c} 5\cr 0\cr 1 \end{array}\right].$$
Express $\vec{x}$ as a linear combination of $\vec{v}_1$, $\vec{v}_2$, and $\vec{v}_3$, and find $A\vec{x}$.

$\vec{x}=$ $\vec{v}_1+$ $\vec{v}_2+$ $\vec{v}_3$.

$A\vec{x}=$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$