**Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix.**\[\begin{bmatrix}6 & 1 & -3 \\6 & -1 & 0 \\6 & -6 & 5\end{bmatrix}; \quad \lambda = 2, 3, 5\]---Select the correct choice below and, if necessary, fill in the answer box to complete your choice.- **A.** For $ P = \, \boxed{\,}$, $ D = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix} $. (Simplify your answer.)- **B.** The matrix cannot be diagonalized.

Answered: Image /qna-images/answer/01c6f5d9-7df1-42a6-85eb-9475b0b056d3.jpg

Answered: 6 1 -3 0; λ = 2,3,5 6-1 6-6 5

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

**Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix.**

\[
\begin{bmatrix}
6 & 1 & -3 \\
6 & -1 & 0 \\
6 & -6 & 5
\end{bmatrix}; \quad \lambda = 2, 3, 5
\]

---

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- **A.**
For $ P = \, \boxed{\,}$, $ D = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix} $.
(Simplify your answer.)

- **B.**
The matrix cannot be diagonalized.

Expert Solution

Step 1: To find the eigenvector:

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