Make a change of variable, x = Py, that transforms the following quadratic form into one with no cross-product terms. -10x-10x-10x-10x²+8x1x3+4x1x4+4x2x3 + 8x2x4 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Problem #6: Make a change of variable, x = Py, that transforms the following quadratic form into one with no cross-product
terms.
-10x-10x-10x-10x+8x1x3 + 4x1x4 + 4x2 x3 + 8x2x4
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.
Transcribed Image Text:Problem #6: Make a change of variable, x = Py, that transforms the following quadratic form into one with no cross-product terms. -10x-10x-10x-10x+8x1x3 + 4x1x4 + 4x2 x3 + 8x2x4 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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