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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?