In Certain Cases, There Is a Nonzero Vector $\vec{v}$ And a Scalar

Short Answer

In certain cases, there is a nonzero vector $\vec{v}$ and a scalar $\lambda$ for a matrix $\mathbf{A}$ such that $\mathbf{A} \vec{v}=\lambda \vec{v}$ . The vector $\vec{v}$ is called an eigenvector of $\mathbf{A}$ with eigenvalue $\lambda$ . Let $\mathbf{A}=\left(\begin{array}{cc}1 & 2 \\ 6 & -3\end{array}\right)$ with eigenvector $\vec{v}=(3,-9)$ . What is its eigenvalue?