(a) Let A be a 2 x 2-matrix. Prove that A² is a linear combination of A and I. (b) Given an example of a 3 × 3-matrix A such that A² is not a linear combination of A and I.
(a) Let A be a 2 x 2-matrix. Prove that A² is a linear combination of A and I. (b) Given an example of a 3 × 3-matrix A such that A² is not a linear combination of A and I.
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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Transcribed Image Text:**Exercise 8.10.3**
(a) Let \( A \) be a \( 2 \times 2 \)-matrix. Prove that \( A^2 \) is a linear combination of \( A \) and \( I \).
(b) Give an example of a \( 3 \times 3 \)-matrix \( A \) such that \( A^2 \) is not a linear combination of \( A \) and \( I \).
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