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) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1, 12 and r3. Find a matrix P such that the change of variables x = Py transforms the quadratic form into one with no cross-product term. Write the new quadratic form with no cross-product term. Find a vector x such that Q(x) is negative.

) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1, 12 and r3. Find a matrix P such that the change of variables x = Py transforms the quadratic form into one with no cross-product term. Write the new quadratic form with no cross-product term. Find a vector x such that Q(x) is negative.

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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) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1, 12 and r3. Find a matrix P such that the change of variables x = Py transforms the quadratic form into one with no cross-product term. Write the new quadratic form with no cross-product term. Find a vector x such that Q(x) is negative.
Transcribed Image Text:) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1, 12 and r3. Find a matrix P such that the change of variables x = Py transforms the quadratic form into one with no cross-product term. Write the new quadratic form with no cross-product term. Find a vector x such that Q(x) is negative.
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