3 -1 Let B 7 -5 1 6. -6 2 Find all eigenvalues and a maximal set S of linearly independent eigenvectors for B. Is B diagonalizable? If not, explain why, and if so, find a matrix P such that P-'BP is diagonal and verify that it is.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Please use the following:

- The union of the bases for all eigenspaces is a maximal linearly independent set of eigenvectors.

- The matrix (or linear operator) is diagonalizable if and only if the number of vectors in this set is equal to the size of the matrix (or the dimension of the vector space).

-1 1
Let B
7 -5 1
6 -6 2
Find all eigenvalues and a maximal set S of linearly independent eigenvectors for B.
Is B diagonalizable? If not, explain why, and if so, find a matrix P such that P-'BP
is diagonal and verify that it is.
Transcribed Image Text:-1 1 Let B 7 -5 1 6 -6 2 Find all eigenvalues and a maximal set S of linearly independent eigenvectors for B. Is B diagonalizable? If not, explain why, and if so, find a matrix P such that P-'BP is diagonal and verify that it is.
Expert Solution
steps

Step by step

Solved in 8 steps

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,