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Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not need to do this in Sage and can type your answer directly onto your document. b. Find the maximum and minimum values of q(u) among all unit vectors u and describe the directions in which they occur. For part (b),

Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not need to do this in Sage and can type your answer directly onto your document. b. Find the maximum and minimum values of q(u) among all unit vectors u and describe the directions in which they occur. For part (b),

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: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not need to do this in Sage and can type your answer directly onto your document. b. Find the maximum and minimum values of q(u) among all unit vectors u and describe the directions in which they occur. For part (b),
Transcribed Image Text:Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not need to do this in Sage and can type your answer directly onto your document. b. Find the maximum and minimum values of q(u) among all unit vectors u and describe the directions in which they occur. For part (b),
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