Given: syn
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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Question
Transcribed Image Text:Given: symmetric matrix B =
2
-1
0
0
-1
0
0
2 -1
2
2
0
0 -1
E MA
(a) Find the eigenvalues of B and determine their algebraic multiplicities.
(b) Find orthonormal bases for the eigenspaces of B associated to each eigenvalue of B. Determine
the geometric multiplicities of each eigenvalue of B.
(c) Find a diagonal matrix D € M4 and an orthogonal matrix P € M4 such that PTBP = D.
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