5. A linear transformation T: RR3 is represented by the matrix 2 -1/2 7/2 1/2 -1/2 1/2 5/2, AT = (a) If B (1,0, 1)', (1, 1,0)', (0, 1, 1)'), what is the matrix A" representing the linear transforma- tion T with respect to the ordered basis B? (Hint: Question 1 of Exercises 1 may help.] (b) Given that C= identity matrix I3. Why does that happen? (2,0, 2)', (3, 3, 0)', (1,4, 3)') is also an ordered basis, show that A is the
5. A linear transformation T: RR3 is represented by the matrix 2 -1/2 7/2 1/2 -1/2 1/2 5/2, AT = (a) If B (1,0, 1)', (1, 1,0)', (0, 1, 1)'), what is the matrix A" representing the linear transforma- tion T with respect to the ordered basis B? (Hint: Question 1 of Exercises 1 may help.] (b) Given that C= identity matrix I3. Why does that happen? (2,0, 2)', (3, 3, 0)', (1,4, 3)') is also an ordered basis, show that A is the
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
2
![5.
A linear transformation T: R → R' is represented by the matrix
2
1
-1/2 7/2 1/2
-1/2 1/2 5/2,
AT
(a) If B = (1,0, 1), (1,1,0)', (0, 1, 1)'), what is the matrix A" representing the linear transforma-
tion T with respect to the ordered basis B? [Hint: Question 1 of Exercises 1 may help.]
%3D
(b) Given that C = ((2,0, 2)', (3, 3,0)', (1, 4, 3)') is also an ordered basis, show that A is the
identity matrix 13. Why does that happen?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3714a945-ac01-47f9-a1fa-0e9444c8d05e%2F0e4064b1-b136-4477-a6ca-4d317bfd4dca%2Fkzd7po_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.
A linear transformation T: R → R' is represented by the matrix
2
1
-1/2 7/2 1/2
-1/2 1/2 5/2,
AT
(a) If B = (1,0, 1), (1,1,0)', (0, 1, 1)'), what is the matrix A" representing the linear transforma-
tion T with respect to the ordered basis B? [Hint: Question 1 of Exercises 1 may help.]
%3D
(b) Given that C = ((2,0, 2)', (3, 3,0)', (1, 4, 3)') is also an ordered basis, show that A is the
identity matrix 13. Why does that happen?
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