Let A be the matrix of the quadratic form below. It can be shown that the eigenvalues of A are 4, 7, and 10. 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. 7x국 + 6x글 +8xg-4x12 + 4x1 x3 Which of the following matrices can be used in x = Py to produce a quadratic form with no cross-product term? O A. В. OC. 2 6 3 2 1 2 2 7 7 3 V5 V5 2 6 2 1 1 7 3 V5 V5 6 1 2 2 0 - 1 - - 3 -- 7 7 7 The corresponding quadratic form is y'Dy = (Simplify your answer.)

Let A be the matrix of the quadratic form below. It can be shown that the eigenvalues of A are 4, 7, and 10. 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. 7x국 + 6x글 +8xg-4x12 + 4x1 x3 Which of the following matrices can be used in x = Py to produce a quadratic form with no cross-product term? O A. В. OC. 2 6 3 2 1 2 2 7 7 3 V5 V5 2 6 2 1 1 7 3 V5 V5 6 1 2 2 0 - 1 - - 3 -- 7 7 7 The corresponding quadratic form is y'Dy = (Simplify your answer.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 27EQ

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