Eigenvalues and Eigenvectors of Symmetric Matrices

Practice Questions

Linear Algebra › Eigenvalues and Eigenvectors of Symmetric Matrices

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$\begin{align*}&\text{Find any and all eigenvalues for the matrix }\&A=\begin{bmatrix}-9&-2\-2&-2\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the eigenvalues for the matrix }\&A=\begin{bmatrix}7&8\8&-10\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Calculate the eigenvalues for the matrix }\&\begin{bmatrix}-5&17&-20\17&-3&-2\-20&-2&12\end{bmatrix}\end{align*}$

$G = \begin{bmatrix} b & b \ b & b \end{bmatrix}$

Give the set of eigenvalues of in terms of , if applicable.

$C= \begin{bmatrix} 4 & a \ a & 8 \end{bmatrix}$ ,

where is a real number.

For to have two real eigenvalues, what must be true for ?

$\begin{align*}&\text{Find any and all eigenvalues for the matrix }\&A=\begin{bmatrix}-13&10&-11\10&-9&11\-11&11&-17\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find any and all eigenvalues for the matrix }\&A=\begin{bmatrix}3&2&15\2&-7&-16\15&-16&-1\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find any and all eigenvalues for the matrix }\&A=\begin{bmatrix}-16&-16\-16&-4\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Calculate the eigenvalues for the matrix }\&\begin{bmatrix}-15&8\8&1\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Calculate the eigenvalues for the matrix }\&\begin{bmatrix}-14&4\4&-19\end{bmatrix}\end{align*}$

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