PS3.3 (NO MATLAB) Recall that a square n x n matrix is invertible if and only if it is row equivalent to the identity matrix In. (a) Using language from Section 3.1, list three facts that must be true about the columns of an invertible matrix A. (b) If T: R² R2 is the linear transformation that rotates the plane counter-clockwise π/2 radians about the origin, the standard matrix A for T is invertible. Give a geometric description for how A-1 would transform the plane. That is, explain in words what A-1 should do "visually" to the plane.
PS3.3 (NO MATLAB) Recall that a square n x n matrix is invertible if and only if it is row equivalent to the identity matrix In. (a) Using language from Section 3.1, list three facts that must be true about the columns of an invertible matrix A. (b) If T: R² R2 is the linear transformation that rotates the plane counter-clockwise π/2 radians about the origin, the standard matrix A for T is invertible. Give a geometric description for how A-1 would transform the plane. That is, explain in words what A-1 should do "visually" to the plane.
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 solve both parts correctly and handwritten
![4.1 Exercises
PS3.1 (MATLAB) Consider the following linear transformations:
-
• T: R² R² is the linear transformation that rotates the plane 7/3 radians counterclockwise about
the origin
• S: R² → R² is the linear transformation that reflects the plane about the line y = -x
• U: R² → R² is the linear transformation that stretches the plane horizontally by a factor of 3
(a) Find the standard motriv 4 for T
[1
-1]
(1212121
(a) B
(b) C =
12
3
4 5
6
7
6 9 12 15
1
1
1
[1 2 -3 0
1
(c) D = 1 2
(d) E=
36-5
1
1
1
2 0
3
4 -2
1
1 5
16
1 4
1]
4
7
6
10 13
21
20
23
0
3 35 0 126
T10
A co tota
-4 56 55 252
PS3.3 (NO MATLAB) Recall that a square n x n matrix is invertible if and only if it is row equivalent to the
identity matrix In.
(a) Using language from Section 3.1, list three facts that must be true about the columns of an invertible
matrix A.
(b) If T: R² R² is the linear transformation that rotates the plane counter-clockwise π/2 radians about
the origin, the standard matrix A for T is invertible. Give a geometric description for how A-¹ would
transform the plane. That is, explain in words what A-1 should do "visually" to the plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feed3e073-f74a-48e7-90aa-d2f42ac0bd95%2F27953651-3cbe-404c-b95c-b2910cd472c0%2F3l488uq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.1 Exercises
PS3.1 (MATLAB) Consider the following linear transformations:
-
• T: R² R² is the linear transformation that rotates the plane 7/3 radians counterclockwise about
the origin
• S: R² → R² is the linear transformation that reflects the plane about the line y = -x
• U: R² → R² is the linear transformation that stretches the plane horizontally by a factor of 3
(a) Find the standard motriv 4 for T
[1
-1]
(1212121
(a) B
(b) C =
12
3
4 5
6
7
6 9 12 15
1
1
1
[1 2 -3 0
1
(c) D = 1 2
(d) E=
36-5
1
1
1
2 0
3
4 -2
1
1 5
16
1 4
1]
4
7
6
10 13
21
20
23
0
3 35 0 126
T10
A co tota
-4 56 55 252
PS3.3 (NO MATLAB) Recall that a square n x n matrix is invertible if and only if it is row equivalent to the
identity matrix In.
(a) Using language from Section 3.1, list three facts that must be true about the columns of an invertible
matrix A.
(b) If T: R² R² is the linear transformation that rotates the plane counter-clockwise π/2 radians about
the origin, the standard matrix A for T is invertible. Give a geometric description for how A-¹ would
transform the plane. That is, explain in words what A-1 should do "visually" to the plane.
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