[1 2 8. Let A = and define Q : R² → R by Q(x) = x"Ax. 2 1 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. (d) For each eigenvalue, state its algebraic and geometric multiplicity. (e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A. (f) Is the quadratic form Q positive definite, negative definite, or neither? (g) Is the conic section defined by the equation Q(x) = 1 an ellipse or an hyperbola? Why?

[1 2 8. Let A = and define Q : R² → R by Q(x) = x"Ax. 2 1 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. (d) For each eigenvalue, state its algebraic and geometric multiplicity. (e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A. (f) Is the quadratic form Q positive definite, negative definite, or neither? (g) Is the conic section defined by the equation Q(x) = 1 an ellipse or an hyperbola? Why?

Name: Need help with part (g). Thank you :) [1 28. Let A =and define Q : R²→
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Description: Need help with part (g). Thank you :) [1 28. Let A =and define Q : R²→ R by Q(x) = x"Ax.2 1(a) Find the characteristic polynomial of A.(b) Find the eigenvalues of A.(c) Find a basis for each eigenspace of A.(d) For each eigenvalue, state its algebrai

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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