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Consider the following matrix: A-() 1. Determine whether A is diagonalizable over C. If so, diagonalize it.

Consider the following matrix: A-() 1. Determine whether A is diagonalizable over C. If so, diagonalize it.

Advanced Engineering Mathematics
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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Consider the following matrix: A = 5 4 1. Determine whether A is diagonalizable over C. If so, diagonalize it. 2. Find an invertible matrix Q € Mat22(R), and real numbers r, 0 €R such that 0 <r and (cos(0) - sin Q-1. A · Q = r · sin(8) cos(8) ) 3. Use your answer from part (2) to find A14. Hint: Recall that for an invertible n x n matrix P and any n x n matrix B, that one has (P ·B · P-!)k = P · B* · P-1 for any natural number k.
Transcribed Image Text:Consider the following matrix: A = 5 4 1. Determine whether A is diagonalizable over C. If so, diagonalize it. 2. Find an invertible matrix Q € Mat22(R), and real numbers r, 0 €R such that 0 <r and (cos(0) - sin Q-1. A · Q = r · sin(8) cos(8) ) 3. Use your answer from part (2) to find A14. Hint: Recall that for an invertible n x n matrix P and any n x n matrix B, that one has (P ·B · P-!)k = P · B* · P-1 for any natural number k.
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