5 Let A = -2 0 Find two different diagonal matrices D and the corresponding matrix P such that A = PDP-¹. D1 = D2 = Note: 0 0 0 。 P1 = 세 P =
5 Let A = -2 0 Find two different diagonal matrices D and the corresponding matrix P such that A = PDP-¹. D1 = D2 = Note: 0 0 0 。 P1 = 세 P =
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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![Let \( A = \begin{bmatrix} 5 & 3 \\ -2 & 0 \end{bmatrix} \).
Find two different diagonal matrices \( D \) and the corresponding matrix \( P \) such that \( A = PDP^{-1} \).
\[
D_1 = \begin{bmatrix} \boxed{} & 0 \\ 0 & \boxed{} \end{bmatrix}
\quad
P_1 = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix}
\]
\[
D_2 = \begin{bmatrix} \boxed{} & 0 \\ 0 & \boxed{} \end{bmatrix}
\quad
P_2 = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix}
\]
Note:
- The task is to find diagonal matrices \( D_1 \) and \( D_2 \) and matrices \( P_1 \) and \( P_2 \) such that \( A = P_1 D_1 P_1^{-1} \) and \( A = P_2 D_2 P_2^{-1} \).
- The \( \boxed{} \) symbols indicate where values need to be calculated or inserted.
The matrices \( D_1 \) and \( D_2 \) represent diagonalized forms of \( A \), while \( P_1 \) and \( P_2 \) are the matrices of eigenvectors corresponding to each diagonalized form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66642e03-4e4a-4c87-8e6d-75cae92b5ebf%2Ffa8205a0-1ee2-4026-b27d-8385bc968dba%2Fvi0hkif_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( A = \begin{bmatrix} 5 & 3 \\ -2 & 0 \end{bmatrix} \).
Find two different diagonal matrices \( D \) and the corresponding matrix \( P \) such that \( A = PDP^{-1} \).
\[
D_1 = \begin{bmatrix} \boxed{} & 0 \\ 0 & \boxed{} \end{bmatrix}
\quad
P_1 = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix}
\]
\[
D_2 = \begin{bmatrix} \boxed{} & 0 \\ 0 & \boxed{} \end{bmatrix}
\quad
P_2 = \begin{bmatrix} \boxed{} & \boxed{} \\ \boxed{} & \boxed{} \end{bmatrix}
\]
Note:
- The task is to find diagonal matrices \( D_1 \) and \( D_2 \) and matrices \( P_1 \) and \( P_2 \) such that \( A = P_1 D_1 P_1^{-1} \) and \( A = P_2 D_2 P_2^{-1} \).
- The \( \boxed{} \) symbols indicate where values need to be calculated or inserted.
The matrices \( D_1 \) and \( D_2 \) represent diagonalized forms of \( A \), while \( P_1 \) and \( P_2 \) are the matrices of eigenvectors corresponding to each diagonalized form.
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