9.4 Find a matrix P and a diagonal matrix D such that P-¹AP = D. 9.5 Find A23. (You may write 223, for example, as it is without calculating its va 9.6 Use the above to solve the following system of differential equations: 3 y₁ = x₁ + 2x2

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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please do 9.4 and 9.5 and 9.6
QUESTION 9
12
Let A =
· (2²).
21
9.1 Find the eigenvalues of A.
9.2 Find bases for the eigenspaces of A.
9.3 Is A diagonalisable? Give reasons.
9.4 Find a matrix P and a diagonal matrix D such that P-¹AP = D.
9.5 Find A23. (You may write 223, for example, as it is without calculating its value.)
9.6 Use the above to solve the following system of differential equations:
3
= 21+22
y₂ = 2x1 + x₂
Transcribed Image Text:QUESTION 9 12 Let A = · (2²). 21 9.1 Find the eigenvalues of A. 9.2 Find bases for the eigenspaces of A. 9.3 Is A diagonalisable? Give reasons. 9.4 Find a matrix P and a diagonal matrix D such that P-¹AP = D. 9.5 Find A23. (You may write 223, for example, as it is without calculating its value.) 9.6 Use the above to solve the following system of differential equations: 3 = 21+22 y₂ = 2x1 + x₂
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