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Suppose A is a symmetric 2 x 2 matrix and we know that A 4-4 = and det(A) = 6. PART A: Solve for A. Hint 1: Since A is symmetric, it is orthogonally diagonalizable so A = QDQT. Hint 2: For symmetric matrices, eigenvectors from different eigenvalues have a special property. PART B: Since A is 2 × 2 it transforms the unit circle in R² into an ellipse. Since A is symmetric, the ellipse is determined by A's eigenvalues and eigenvectors. Provide a sketch of the ellipse.

Suppose A is a symmetric 2 x 2 matrix and we know that A 4-4 = and det(A) = 6. PART A: Solve for A. Hint 1: Since A is symmetric, it is orthogonally diagonalizable so A = QDQT. Hint 2: For symmetric matrices, eigenvectors from different eigenvalues have a special property. PART B: Since A is 2 × 2 it transforms the unit circle in R² into an ellipse. Since A is symmetric, the ellipse is determined by A's eigenvalues and eigenvectors. Provide a sketch of the ellipse.

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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Suppose A is a symmetric 2 x 2 matrix and we know that A 1-4 = and det(A) = 6. PART A: Solve for A. Hint 1: Since A is symmetric, it is orthogonally diagonalizable so A = QDQT. Hint 2: For symmetric matrices, eigenvectors from different eigenvalues have a special property. PART B: Since A is 2 × 2 it transforms the unit circle in R² into an ellipse. Since A is symmetric, the ellipse is determined by A's eigenvalues and eigenvectors. Provide a sketch of the ellipse.
Transcribed Image Text:Suppose A is a symmetric 2 x 2 matrix and we know that A 1-4 = and det(A) = 6. PART A: Solve for A. Hint 1: Since A is symmetric, it is orthogonally diagonalizable so A = QDQT. Hint 2: For symmetric matrices, eigenvectors from different eigenvalues have a special property. PART B: Since A is 2 × 2 it transforms the unit circle in R² into an ellipse. Since A is symmetric, the ellipse is determined by A's eigenvalues and eigenvectors. Provide a sketch of the ellipse.
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