Let A = 3) 22 13 9.1 Find the eigenvalues of A.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
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Let A =
22
1 3
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:
y₁ = 2x₁ + 2x2
y₂ = x1 + 3x₂
Transcribed Image Text:Let A = 22 1 3 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: y₁ = 2x₁ + 2x2 y₂ = x1 + 3x₂
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