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?

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The Answer of 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?

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

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