Solve the corresponding eigenvectors matrix A = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{pmatrix}
MathBot Answer:
The eigenvalues of the matrix are:
\[
\begin{aligned}
\lambda_{1} &= 2\\
\lambda_{2} &= 3\\
\lambda_{3} &= 5
\end{aligned}
\]
The eigenvector \(\begin{bmatrix}1\\0\\0\end{bmatrix}\) is associated with the eigenvalue \(\lambda_{1}\).
The eigenvector \(\begin{bmatrix}0\\1\\0\end{bmatrix}\) is associated with the eigenvalue \(\lambda_{2}\).
The eigenvector \(\begin{bmatrix}0\\0\\1\end{bmatrix}\) is associated with the eigenvalue \(\lambda_{3}\).