(b) The equation 5x² + 5y² - 4xy = 0.5 defines an ellipse on the xy-plane. Find the rotation matrix R = cos sin - sin cos so that the ellipse can be expressed as the weighted sum of the squares. (Note: You don't need to compute 0. Notice that R is an orthogonal matrix. Also, an equation of an ellipse whose major and minor axes are aligned with the x and the y axes has the form += 1.)

(b) The equation 5x² + 5y² - 4xy = 0.5 defines an ellipse on the xy-plane. Find the rotation matrix R = cos sin - sin cos so that the ellipse can be expressed as the weighted sum of the squares. (Note: You don't need to compute 0. Notice that R is an orthogonal matrix. Also, an equation of an ellipse whose major and minor axes are aligned with the x and the y axes has the form += 1.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 15AEXP

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