4. In each part below, A is a 2 x 2 matrix of real numbers (and I is the 2 x 2 identity). (a) Suppose A² – 5A + 61 = 0. Show that any eigenvalue of A must equal either 2 or 3. (b) Suppose A has both 2 and 3 as eigenvalues. Show that A² – 5A+6I = 0. (Hint: Show that each eigenvector belongs to Null(A² – 5A+ 61).) (c) Find an A whose only eigenvalues lie in {2,3} but where A2 -5A+61 0.
4. In each part below, A is a 2 x 2 matrix of real numbers (and I is the 2 x 2 identity). (a) Suppose A² – 5A + 61 = 0. Show that any eigenvalue of A must equal either 2 or 3. (b) Suppose A has both 2 and 3 as eigenvalues. Show that A² – 5A+6I = 0. (Hint: Show that each eigenvector belongs to Null(A² – 5A+ 61).) (c) Find an A whose only eigenvalues lie in {2,3} but where A2 -5A+61 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
100%
i would like help with question 4
Transcribed Image Text:4. In each part below, A is a 2 x 2 matrix of real numbers (and I is the 2 x 2 identity).
(a) Suppose A² – 5A + 61 = 0. Show that any eigenvalue of A must equal either 2
or 3.
(b) Suppose A has both 2 and 3 as eigenvalues. Show that A² – 5A+6I = 0. (Hint:
Show that each eigenvector belongs to Null(A² – 5A+ 61).)
(c) Find an A whose only eigenvalues lie in {2,3} but where A2 -5A+61 0.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
