(17) (a) Consider the following matrix a 1 = ( 4 ) A For which values of a and b is true that A² = I₂ (b) Find A² and A³ (c) Use (b) to find An if n is even and An if n is odd
(17) (a) Consider the following matrix a 1 = ( 4 ) A For which values of a and b is true that A² = I₂ (b) Find A² and A³ (c) Use (b) to find An if n is even and An if n is odd
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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![### Matrix Analysis Question
**Question 17:**
(a) Consider the following matrix
\[ A = \begin{pmatrix}
a & b \\
-b & -a
\end{pmatrix} \]
For which values of \(a\) and \(b\) is it true that \(A^2 = I_2\)?
(b) Find \(A^2\) and \(A^3\).
(c) Use (b) to find \(A^n\) if \(n\) is even and \(A^n\) if \(n\) is odd.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81e8ba16-e7f4-4cb8-bc35-ac7ab5472c5c%2Fba4298fe-88c7-4f39-868d-fa038fc7ebad%2F6jboz4k_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrix Analysis Question
**Question 17:**
(a) Consider the following matrix
\[ A = \begin{pmatrix}
a & b \\
-b & -a
\end{pmatrix} \]
For which values of \(a\) and \(b\) is it true that \(A^2 = I_2\)?
(b) Find \(A^2\) and \(A^3\).
(c) Use (b) to find \(A^n\) if \(n\) is even and \(A^n\) if \(n\) is odd.
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