Make a change of variable, x = Py, that transforms the following quadratic form into one with no cross-product terms. -2x-2x3-8x1x2 +14x₁x3+14x₁x4 +14x₂x3 + 14x2x4-12x3x4 Construct P For the associated quadratic form, enter the eigenvalues in decreasing order (including multiplicities) into the answer box below, separated with commas.

Make a change of variable, x = Py, that transforms the following quadratic form into one with no cross-product terms. -2x-2x3-8x1x2 +14x₁x3+14x₁x4 +14x₂x3 + 14x2x4-12x3x4 Construct P For the associated quadratic form, enter the eigenvalues in decreasing order (including multiplicities) into the answer box below, separated with commas.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 77E

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Make a change of variable, x = Py, that transforms the following quadratic form into one with no cross-product terms. 6x² + 6x² + 8x1x2 + 6x1x3 + 6x1x4 + 6x2x3 + 6x2x4 + 20x3x4 Construct P using the methods of Section 7.1. For the associated quadratic form, enter the eigenvalues in decreasing order (including multiplicities) into the answer box below, separated with commas.
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