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For each quadratic function a) State the matrix of the quadratic form associated with the given equation. b) Determine the eigenvalues of the matrix. c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. 1. Let p = 5. Let q = 8. 5x2 + 8xy + 5y2 − pVZx+qVZy–18 = 0

For each quadratic function a) State the matrix of the quadratic form associated with the given equation. b) Determine the eigenvalues of the matrix. c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. 1. Let p = 5. Let q = 8. 5x2 + 8xy + 5y2 − pVZx+qVZy–18 = 0

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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**For each quadratic function** a) State the matrix of the quadratic form associated with the given equation. b) Determine the eigenvalues of the matrix. c) Construct an orthogonal matrix \( P \) with \( |P| = 1 \) that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. 1. Let \( p = 5 \). Let \( q = 8 \). \( 5x^2 + 8xy + 5y^2 - p\sqrt{2}\,x + q\sqrt{2}\,y - 18 = 0 \)
Transcribed Image Text:**For each quadratic function** a) State the matrix of the quadratic form associated with the given equation. b) Determine the eigenvalues of the matrix. c) Construct an orthogonal matrix \( P \) with \( |P| = 1 \) that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. 1. Let \( p = 5 \). Let \( q = 8 \). \( 5x^2 + 8xy + 5y^2 - p\sqrt{2}\,x + q\sqrt{2}\,y - 18 = 0 \)
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