Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The matrix (- has eigenvalues 26 and -26, and corresponding eigenvectors A= = and 10 -24 -24 -10 ATIVA PL W √13 (3, -2) (2,3) respectively, both of magnitude 1. √13 (a) Write down an orthogonal matrix P and a diagonal matrix D such that PT AP = D. (b) Use your answer to part (a) to find the standard form of the equation of the non-degenerate conic with equation 10x²-48ry - 10y² + 3x - 2y = 0. (c) Hence state whether the conic is an ellipse, a parabola or a hyperbola.

The matrix (- has eigenvalues 26 and -26, and corresponding eigenvectors A= = and 10 -24 -24 -10 ATIVA PL W √13 (3, -2) (2,3) respectively, both of magnitude 1. √13 (a) Write down an orthogonal matrix P and a diagonal matrix D such that PT AP = D. (b) Use your answer to part (a) to find the standard form of the equation of the non-degenerate conic with equation 10x²-48ry - 10y² + 3x - 2y = 0. (c) Hence state whether the conic is an ellipse, a parabola or a hyperbola.

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
See similar textbooks
icon
Related questions
Question
The matrix 10 -24 -24 -10 has eigenvalues 26 and -26, and corresponding eigenvectors (3,-2) 1 and (2,3) respectively, both of magnitude 1. √13 (a) Write down an orthogonal matrix P and a diagonal matrix D such that PT AP = D. A = 20 1 /13 (b) Use your answer to part (a) to find the standard form of the equation of the non-degenerate conic with equation 10.x² - 48ry - 10y² + 3x - 2y = 0. (c) Hence state whether the conic is an ellipse, a parabola or a hyperbola.
Transcribed Image Text:The matrix 10 -24 -24 -10 has eigenvalues 26 and -26, and corresponding eigenvectors (3,-2) 1 and (2,3) respectively, both of magnitude 1. √13 (a) Write down an orthogonal matrix P and a diagonal matrix D such that PT AP = D. A = 20 1 /13 (b) Use your answer to part (a) to find the standard form of the equation of the non-degenerate conic with equation 10.x² - 48ry - 10y² + 3x - 2y = 0. (c) Hence state whether the conic is an ellipse, a parabola or a hyperbola.
Expert Solution
steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS