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2 -6 -3 -6-3 2 -3 2 -6. The eigenvalues of the real symmetric matrix A are X₁ = 7 and A₂ = −7. Let A An orthonormal basis for the eigenspace for A₁ = 7 is B₁ {u₁} where 111 and an orthonormal basis for the eigenspace for A₂ = -7 is B₂ = {1₂, 13} where 112 Thus, if P= 113 then P is orthogonal and PT AP = D. and D

2 -6 -3 -6-3 2 -3 2 -6. The eigenvalues of the real symmetric matrix A are X₁ = 7 and A₂ = −7. Let A An orthonormal basis for the eigenspace for A₁ = 7 is B₁ {u₁} where 111 and an orthonormal basis for the eigenspace for A₂ = -7 is B₂ = {1₂, 13} where 112 Thus, if P= 113 then P is orthogonal and PT AP = D. and D

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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Let A The eigenvalues of the real symmetric matrix A are >₁ = An orthonormal basis for the eigenspace for X₁ = 7 is B₁ 11₁ 3 2 -6 -3 -6-3 2 -3 2 -6 112 Thus, if and an orthonormal basis for the eigenspace for X₂ = -7 is B₂ = = = {U₂, U3} where P 113 7 and A₂ = -7. then P is orthogonal and PT AP = D. {u₁} where and D
Transcribed Image Text:Let A The eigenvalues of the real symmetric matrix A are >₁ = An orthonormal basis for the eigenspace for X₁ = 7 is B₁ 11₁ 3 2 -6 -3 -6-3 2 -3 2 -6 112 Thus, if and an orthonormal basis for the eigenspace for X₂ = -7 is B₂ = = = {U₂, U3} where P 113 7 and A₂ = -7. then P is orthogonal and PT AP = D. {u₁} where and D
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