Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a) Diagonalize the matrix in the form A = SAS-¹, with S a matrix containing the (normalized) eigenvectors and A a diagonal matrix containing the eigenvalues. b) Is the matrix S an orthogonal matrix? Why / why not? c) Using the eigenvalue decomposition computed in a), determine (including a short explanation!) a. the rank of the matrix A. b. the determinant of the matrix A.

a) Diagonalize the matrix in the form A = SAS-¹, with S a matrix containing the (normalized) eigenvectors and A a diagonal matrix containing the eigenvalues. b) Is the matrix S an orthogonal matrix? Why / why not? c) Using the eigenvalue decomposition computed in a), determine (including a short explanation!) a. the rank of the matrix A. b. the determinant of the matrix A.

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

Clear Handwriting and picture please !

Thanks

Consider the matrix A = 2 | 0 a. 1 2 -1 2 4 0 a) Diagonalize the matrix in the form A = SAS-1, with S a matrix containing the (normalized) eigenvectors and A a diagonal matrix containing the eigenvalues. b) Is the matrix S an orthogonal matrix? Why / why not? c) Using the eigenvalue decomposition computed in a), determine (including a short explanation!) the rank of the matrix A. b. the determinant of the matrix A. C. the null space of the matrix A. d) Determine if the matrix B = (A+A¹)´¹ is positive definite, negative definite or indefinite, without computing its eigenvalue decomposition. (Hint: use the elimination method and Hermite's theorem).
Transcribed Image Text:Consider the matrix A = 2 | 0 a. 1 2 -1 2 4 0 a) Diagonalize the matrix in the form A = SAS-1, with S a matrix containing the (normalized) eigenvectors and A a diagonal matrix containing the eigenvalues. b) Is the matrix S an orthogonal matrix? Why / why not? c) Using the eigenvalue decomposition computed in a), determine (including a short explanation!) the rank of the matrix A. b. the determinant of the matrix A. C. the null space of the matrix A. d) Determine if the matrix B = (A+A¹)´¹ is positive definite, negative definite or indefinite, without computing its eigenvalue decomposition. (Hint: use the elimination method and Hermite's theorem).
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

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