Find the eigenvalues $\lambda_1 < \lambda_2 < \lambda_3$ and associated unit eigenvectors $\vec{u}_1, \vec{u}_2, \vec{u}_3$ of the symmetric matrix \[A = \begin{bmatrix} 0 & 0 & 9 \\ 0 & -6 & 0 \\ 9 & 0 & 0 \end{bmatrix}.\]**The eigenvalue $\lambda_1 =$** $\_\_\_\_\_\_\_$ has associated unit eigenvector $\vec{u}_1 =$ \[\begin{bmatrix} \_\_\_\_ \\ \_\_\_\_ \\ \_\_\_\_ \end{bmatrix}.\]**The eigenvalue $\lambda_2 =$** $\_\_\_\_\_\_\_$ has associated unit eigenvector $\vec{u}_2 =$ \[\begin{bmatrix} \_\_\_\_ \\ \_\_\_\_ \\ \_\_\_\_ \end{bmatrix}.\]**The eigenvalue $\lambda_3 =$** $\_\_\_\_\_\_\_$ has associated unit eigenvector $\vec{u}_3 =$ \[\begin{bmatrix} \_\_\_\_ \\ \_\_\_\_ \\ \_\_\_\_ \end{bmatrix}.\]*Note: The eigenvectors above form an orthonormal eigenbasis for $ A $.*

The given matrix is A=0090-60900. Find the eigenvalues of A as follows.…

Find the eigenvalues A, < A2 < Ag and associated unit eigenvectors ū1, üz, üz of the symmetric matrix Го 9 A = 0 -6 0 9. 0. The eigenvalue A, has associated unit eigenvector u The eigenvalue A, = has associated unit eigenvector üz The eigenvalue A3 has associated unit eigenvector ūz Note: The eigenvectors above form an orthonormal eigenbasis for A.

Find the eigenvalues A, < A2 < Ag and associated unit eigenvectors ū1, üz, üz of the symmetric matrix Го 9 A = 0 -6 0 9. 0. The eigenvalue A, has associated unit eigenvector u The eigenvalue A, = has associated unit eigenvector üz The eigenvalue A3 has associated unit eigenvector ūz Note: The eigenvectors above form an orthonormal eigenbasis for A.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the eigenvalues $\lambda_1 < \lambda_2 < \lambda_3$ and associated unit eigenvectors $\vec{u}_1, \vec{u}_2, \vec{u}_3$ of the symmetric matrix

\[
A = \begin{bmatrix}
0 & 0 & 9 \\
0 & -6 & 0 \\
9 & 0 & 0
\end{bmatrix}.
\]

**The eigenvalue $\lambda_1 =$** $\_\_\_\_\_\_\_$ has associated unit eigenvector $\vec{u}_1 =$
\[
\begin{bmatrix}
\_\_\_\_ \\
\_\_\_\_ \\
\_\_\_\_
\end{bmatrix}.
\]

**The eigenvalue $\lambda_2 =$** $\_\_\_\_\_\_\_$ has associated unit eigenvector $\vec{u}_2 =$
\[
\begin{bmatrix}
\_\_\_\_ \\
\_\_\_\_ \\
\_\_\_\_
\end{bmatrix}.
\]

**The eigenvalue $\lambda_3 =$** $\_\_\_\_\_\_\_$ has associated unit eigenvector $\vec{u}_3 =$
\[
\begin{bmatrix}
\_\_\_\_ \\
\_\_\_\_ \\
\_\_\_\_
\end{bmatrix}.
\]

*Note: The eigenvectors above form an orthonormal eigenbasis for $ A $.*

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