Find a 3 x 3 symmetric matrix A that has eigenvalues -1 and 2 and eigenspaces E-1 = span{(1,1,0)} and E₂ = span{(0, 0, 1), (1, -1, 1)}. Make sure you show all your working, [Hint: Find a diagonal matrix D and a matrix P that orthogonally diagonalises A and then use these to calculate A.]
Find a 3 x 3 symmetric matrix A that has eigenvalues -1 and 2 and eigenspaces E-1 = span{(1,1,0)} and E₂ = span{(0, 0, 1), (1, -1, 1)}. Make sure you show all your working, [Hint: Find a diagonal matrix D and a matrix P that orthogonally diagonalises A and then use these to calculate A.]
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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![Find a 3 x 3 symmetric matrix A that has eigenvalues -1 and 2 and
eigenspaces E_1 = span{(1, 1,0)} and E₂ = span{(0, 0, 1), (1, -1, 1)}.
Make sure you show all your working,
[Hint: Find a diagonal matrix D and a matrix P that orthogonally
diagonalises A and then use these to calculate A.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ac09755-9639-4075-b6f1-d2ae73f82d81%2Fecc659c1-40e6-49f5-9e12-d64a2c6d43a8%2Fprbzx6h_processed.png&w=3840&q=75)
Transcribed Image Text:Find a 3 x 3 symmetric matrix A that has eigenvalues -1 and 2 and
eigenspaces E_1 = span{(1, 1,0)} and E₂ = span{(0, 0, 1), (1, -1, 1)}.
Make sure you show all your working,
[Hint: Find a diagonal matrix D and a matrix P that orthogonally
diagonalises A and then use these to calculate A.]
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