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(b) Let A be a 3 x 3 real symmetric matrix with three distinct real eigenvalues. It is known that eigenspaces for two of the eigenvalues are {(t, 0, –t)} and {(t, –2t, t)}. What is the eigenspace for the third eigenvalue? Explain your answer carefully.

(b) Let A be a 3 x 3 real symmetric matrix with three distinct real eigenvalues. It is known that eigenspaces for two of the eigenvalues are {(t, 0, –t)} and {(t, –2t, t)}. What is the eigenspace for the third eigenvalue? Explain your answer carefully.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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(a) Which of the following matrices are orthogonal matrices? Explain your answer. BEB 1 00 1 1 -1 1 2 3 0 1 0 1 4 5 6 0 0 1 1 -1 1 7 89 (b) Let A be a 3 × 3 real symmetric matrix with three distinct real eigenvalues. It is known that eigenspaces for two of the eigenvalues are {(t, 0, –t)} and {(t, -2t, t)}. What is the | eigenspace for the third eigenvalue? Explain your answer carefully.
Transcribed Image Text:(a) Which of the following matrices are orthogonal matrices? Explain your answer. BEB 1 00 1 1 -1 1 2 3 0 1 0 1 4 5 6 0 0 1 1 -1 1 7 89 (b) Let A be a 3 × 3 real symmetric matrix with three distinct real eigenvalues. It is known that eigenspaces for two of the eigenvalues are {(t, 0, –t)} and {(t, -2t, t)}. What is the | eigenspace for the third eigenvalue? Explain your answer carefully.
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