c) Show that eigenvectors of [T]B exhibit an orthonormal basis of Rt.
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
Question
please send handwritten solution for part c
![Problem 3
Let T: Max2(R) → M2x2(R) be the linear operator defined as
a b
T
с d
За - 2с + 4d
-2a + 6c + 2d 4a + 2c + 3d
1 0
0 1
0 0
0 0
Let B =
denote the standard basis of M2x2(R).
0 0
0 0
1 0
0 1
a) Find [T]B. Determine the characteristic polynomial of [TB, i.e. PT(A). Find the eigenval-
ues of [T)B and determine the algebraic multiplicity of each eigenvalue.
(Hint: Eigenvalues are -2, 0 and 7.)
b) Determine a basis for each eigenspace ET, (A) of (T]B and determine the geometric multiplic-
ity of each eigenvalue. Find it in increasing order of the eigenvalues.
c) Show that eigenvectors of [T)B exhibit an orthonormal basis of R4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26a77bed-bbca-410f-a4fd-d651a789a370%2Fa8813acb-1d84-4da4-9d05-e40fd8e21aed%2F1du6biq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3
Let T: Max2(R) → M2x2(R) be the linear operator defined as
a b
T
с d
За - 2с + 4d
-2a + 6c + 2d 4a + 2c + 3d
1 0
0 1
0 0
0 0
Let B =
denote the standard basis of M2x2(R).
0 0
0 0
1 0
0 1
a) Find [T]B. Determine the characteristic polynomial of [TB, i.e. PT(A). Find the eigenval-
ues of [T)B and determine the algebraic multiplicity of each eigenvalue.
(Hint: Eigenvalues are -2, 0 and 7.)
b) Determine a basis for each eigenspace ET, (A) of (T]B and determine the geometric multiplic-
ity of each eigenvalue. Find it in increasing order of the eigenvalues.
c) Show that eigenvectors of [T)B exhibit an orthonormal basis of R4.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
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,
