(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
icon
Related questions
Question
100%
### 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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,