(a) Find all eigenvalues of (Hint: All eigenvalues of this lare real numbers.) (b) For each eigenvalue, find a basis for its corresponding eigenspace. Perform the Itasks (a) and (b) qon the matrix [o 1 0 -2 1 1 В - 1 0 -3 0 6

(a) Find all eigenvalues of (Hint: All eigenvalues of this lare real numbers.) (b) For each eigenvalue, find a basis for its corresponding eigenspace. Perform the Itasks (a) and (b) qon the matrix [o 1 0 -2 1 1 В - 1 0 -3 0 6

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

### Eigenvalues and Eigenspaces

**(a)** Find all eigenvalues of matrix $ B $. *(Hint: All eigenvalues of this matrix are real numbers.)*

**(b)** For each eigenvalue, find a basis for its corresponding eigenspace.

Perform the tasks (a) and (b) on the matrix:

\[
B = \begin{bmatrix}
0 & 1 & 0 & -2 \\
0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 \\
0 & -3 & 0 & 6
\end{bmatrix}
\]

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