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Consider the quadratic form given by Q(r, y) = 8x2 + 6xy. 1. Give the symmetric matrix associated with Q and find its eigenvalues.

Consider the quadratic form given by Q(r, y) = 8x2 + 6xy. 1. Give the symmetric matrix associated with Q and find its eigenvalues.

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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hello, would you please help me with this? Thanks in advance.
Consider the quadratic form given by Q(r, y) = 8r + 6xy. 1. Give the symmetric matrix associated with Q and find its eigenvalues. 2. Give unit vectors X, and X, which determine the axes of symmetry for the associated curve CH : Q(r, y) = 0, and give the form of Q associated with these new coordinate axes, that is, the form Q(u, v) = A1u² + A2v². 3. Classify CH (as an ellipse, hyperbola, empty curve, etc) and draw a sketch. 4. Give a formula for the locus of CH in terms of u and v.
Transcribed Image Text:Consider the quadratic form given by Q(r, y) = 8r + 6xy. 1. Give the symmetric matrix associated with Q and find its eigenvalues. 2. Give unit vectors X, and X, which determine the axes of symmetry for the associated curve CH : Q(r, y) = 0, and give the form of Q associated with these new coordinate axes, that is, the form Q(u, v) = A1u² + A2v². 3. Classify CH (as an ellipse, hyperbola, empty curve, etc) and draw a sketch. 4. Give a formula for the locus of CH in terms of u and v.
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