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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.

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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Problem #7: 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.
Transcribed Image Text:Problem #7: 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.
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