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quadrato form below. It can be shown that the eigenvalues of A are 6, 9, and that the change of variable x=Py transforms x Ax into a quadratic form with no cross-product term. Give P and the new quadratic form. 9x² +8x3+10x3-4x₁x2 + 4x₁xg

quadrato form below. It can be shown that the eigenvalues of A are 6, 9, and that the change of variable x=Py transforms x Ax into a quadratic form with no cross-product term. Give P and the new quadratic form. 9x² +8x3+10x3-4x₁x2 + 4x₁xg

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 be the matrix of the quadratic form below. It can be shown that the eigenvalues of A are 6, 9, and 12. Find an orthogonal matrix P such that the change of variable x=Py transforms x Ax into a quadratic form with no cross-product term. Give P and the new quadratic form. 9x² +8x2 +10x3-4x₁x₂ + 4x₁ x3 Which of the following matrices can be used in x-Py to produce a quadratic form with no cross-product term? OB. OC. A 2 3 1 3 2 3 2 2 The corresponding quadratic form is y' Dy= (Simplify your answer.) 1 √/2 CIT √2 1 1 √/2 √2 0 0 0 6 3 7
Transcribed Image Text:↑ Let A be the matrix of the quadratic form below. It can be shown that the eigenvalues of A are 6, 9, and 12. Find an orthogonal matrix P such that the change of variable x=Py transforms x Ax into a quadratic form with no cross-product term. Give P and the new quadratic form. 9x² +8x2 +10x3-4x₁x₂ + 4x₁ x3 Which of the following matrices can be used in x-Py to produce a quadratic form with no cross-product term? OB. OC. A 2 3 1 3 2 3 2 2 The corresponding quadratic form is y' Dy= (Simplify your answer.) 1 √/2 CIT √2 1 1 √/2 √2 0 0 0 6 3 7
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