Find the eigen values and eigenvector for the matrix A=
[■(2&2&-2@1&3&-1@-1&1& 1)]
MathBot Answer:
The eigenvalues of the matrix are:
\[
\begin{aligned}
\lambda_{1} &= 0\\
\lambda_{2} &= 2\\
\lambda_{3} &= 4
\end{aligned}
\]
The eigenvector \(\begin{bmatrix}1\\0\\1\end{bmatrix}\) is associated with the eigenvalue \(\lambda_{1}\).
The eigenvector \(\begin{bmatrix}0\\1\\1\end{bmatrix}\) is associated with the eigenvalue \(\lambda_{2}\).
The eigenvector \(\begin{bmatrix}1\\1\\0\end{bmatrix}\) is associated with the eigenvalue \(\lambda_{3}\).