A b- -1, a-1 n b- 1, a-0 b = 0, a- any real number b = 1, a- 1 b = any real number, a = 1 CCCCC
A b- -1, a-1 n b- 1, a-0 b = 0, a- any real number b = 1, a- 1 b = any real number, a = 1 CCCCC
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
![Determine \( a \) and \( b \) such that \( A \) is idempotent. (Select all that apply.)
\[
A = \begin{bmatrix} 1 & 0 \\ a & b \end{bmatrix}
\]
Options:
- \( b = -1, \, a = 1 \)
- \( b = 1, \, a = 0 \)
- \( b = 0, \, a = \) any real number
- \( b = 1, \, a = 1 \)
- \( b = \) any real number, \( a = 1 \) (incorrect)
Explanation:
An idempotent matrix satisfies the condition \( A^2 = A \). You need to evaluate each option based on this property to determine the correct pairs of \( a \) and \( b \). The final option is marked as incorrect, indicating it does not satisfy the idempotent condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F350a872a-0bb3-4218-bc06-9a68f5ae92af%2Ffab9bbf9-b0a1-40e5-823b-f9c11fd5a2db%2Fhbcqd99_processed.png&w=3840&q=75)
Transcribed Image Text:Determine \( a \) and \( b \) such that \( A \) is idempotent. (Select all that apply.)
\[
A = \begin{bmatrix} 1 & 0 \\ a & b \end{bmatrix}
\]
Options:
- \( b = -1, \, a = 1 \)
- \( b = 1, \, a = 0 \)
- \( b = 0, \, a = \) any real number
- \( b = 1, \, a = 1 \)
- \( b = \) any real number, \( a = 1 \) (incorrect)
Explanation:
An idempotent matrix satisfies the condition \( A^2 = A \). You need to evaluate each option based on this property to determine the correct pairs of \( a \) and \( b \). The final option is marked as incorrect, indicating it does not satisfy the idempotent condition.
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