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(a) Which of the following matrices are orthogonal matrices? Explain your answer. BEB 1 0 0 1 -1 1 2 3 0 1 1 4 5 6 0 0 1 -1 1 7 89 (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.

(a) Which of the following matrices are orthogonal matrices? Explain your answer. BEB 1 0 0 1 -1 1 2 3 0 1 1 4 5 6 0 0 1 -1 1 7 89 (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.

Advanced Engineering Mathematics
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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(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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