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Problem 5. Consider the matrix A = 3 1 3 (a) (b) (c) orthogonal, with det Ao < 0, but with Ao -I. (An example of such an Ao is A.) Find the eigenvalues of Ao, together with their algebraic multiplicities. Show that A is an orthogonal matrix. Compute det A. Let A, be any 3 x 3 matrix with real entries which is both symmetric and For each eigenvalue of Ao, find its geometric multiplicity. What type of transformation is A, (projection, reflection, rotation, . Turning back to A, find an orthonormal eigenbasis for A. )?

Problem 5. Consider the matrix A = 3 1 3 (a) (b) (c) orthogonal, with det Ao < 0, but with Ao -I. (An example of such an Ao is A.) Find the eigenvalues of Ao, together with their algebraic multiplicities. Show that A is an orthogonal matrix. Compute det A. Let A, be any 3 x 3 matrix with real entries which is both symmetric and For each eigenvalue of Ao, find its geometric multiplicity. What type of transformation is A, (projection, reflection, rotation, . Turning back to A, find an orthonormal eigenbasis for A. )?

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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Problem 5. Consider the matrix 2 A = 3 1 3 (a) (b) OShow that A is an orthogonal matrix. Compute det A. Let Ao be any 3 x 3 matrix with real entries which is both symmetric and orthogonal, with det Ao < 0, but with Ao # -I. (An example of such an Ao is A.) Find the eigenvalues of A9, together with their algebraic multiplicities. (d) (e) (f) For each eigenvalue of Ao, find its geometric multiplicity. OWhat type of transformation is Ao (projection, reflection, rotation, ...)? Turning back to A, find an orthonormal eigenbasis for A.
Transcribed Image Text:Problem 5. Consider the matrix 2 A = 3 1 3 (a) (b) OShow that A is an orthogonal matrix. Compute det A. Let Ao be any 3 x 3 matrix with real entries which is both symmetric and orthogonal, with det Ao < 0, but with Ao # -I. (An example of such an Ao is A.) Find the eigenvalues of A9, together with their algebraic multiplicities. (d) (e) (f) For each eigenvalue of Ao, find its geometric multiplicity. OWhat type of transformation is Ao (projection, reflection, rotation, ...)? Turning back to A, find an orthonormal eigenbasis for A.
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