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## Homework Statement

Find the eigenvalues of the matrix ##\begin{bmatrix}

4 & 0 & 0 \\

0 & 0 & 0 \\

1 & 0 & -3

\end{bmatrix}##

## Homework Equations

##Ax=λx##

## The Attempt at a Solution

I'm having some trouble finding the eigenvalues of this matrix.

The eigenvalue of a matrix is a scalar λ such that ##Ax=λx##.

To find the eigenvalue, I tried the following:

##\begin{bmatrix}

4 & 0 & 0 \\

0 & 0 & 0 \\

1 & 0 & -3

\end{bmatrix} \begin{bmatrix}

x_1 \\

x_2\\

x_3

\end{bmatrix} = λ\begin{bmatrix}

x_1 \\

x_2\\

x_3

\end{bmatrix}

=

\begin{bmatrix}

4 & 0 & 0 & λ\\

0 & 0 & 0 & λ\\

1 & 0 & -3 & λ

\end{bmatrix}

##

But that doesn't seem to make any sense to me. Lambda can't be 4, 0, and -2, right?