Week6Worksheet(1).pdf - MXB106 Semester 2 2018 Week 6 Worksheet Workshop Week 6 Eigenvalues and eigenvectors Q5 will be done by the tutor at the end of

# Week6Worksheet(1).pdf - MXB106 Semester 2 2018 Week 6...

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MXB106 Semester 2, 2018 Week 6 Worksheet Workshop Week 6: Eigenvalues and eigenvectors Q5 will be done by the tutor at the end of the workshop 1. If the matrixA=124-1has the eigenvalueλ= 3, show that the vectorv=11Tis the corresponding eigenvector.2. LetAandxbe as follows:A=401232104;x=121Confirm by multiplication thatxis an eigenvector ofA. What is the correspondingeigenvalue?3. LetA=13-3-37-3-66-2(a) Find the characteristic equation forA.(b) Find the eigenvalues forAand their corresponding multiplicities.(c) For each eigenvalue, find the corresponding eigenvectors.4. LetA=1-321(a) Find the characteristic equation forA.(b) Find the eigenvalues forAand their corresponding multiplicities.(c) For each eigenvalue, find the corresponding eigenvectors.5. LetA=2111211121
MXB106 Semester 2, 2018 Week 6 Worksheet Workshop (a) Verify that the characteristic equation ofAis (λ-4)(λ-1)2= 0.(b) Using your result from (a), find the eigenvalues ofAand their corresponding