Linear algebra: please solve last 2 parts of question 3.3 correctly and handwritten 4.1 ExercisesPS3.1 (MATLAB) Consider the following linear transformations:• T: R² → R² is the linear transformation that rotates the plane 7/3 radians counterclockwise aboutthe origin• S: R²R2 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 T24(a) B=(b) C =2[14 576 9 12 15111 13624(c) D=(d) E=[12 -3 012 1 136 -5 141][1 1 112 07613 -1 10132114 -2 20 23015 3 35 0 12616-4 56 55 25214PS3.3 (NO MATLAB) Recall that a square n x n matrix is invertible if and only if it is row equivalent to theidentity matrix In.(a) Using language from Section 3.1, list three facts that must be true about the columns of an invertiblematrix A.(b) If T: R² → R² is the linear transformation that rotates the plane counter-clockwise 7/2 radians aboutthe origin, the standard matrix A for T is invertible. Give a geometric description for how A-¹ wouldtransform the plane. That is, explain in words what A-1 should do "visually" to the plane.

Given: A square n×n matrix is invertible if and only if it is row equivalent to the identity matrix…

Answered: PS3.3 (NO MATLAB) Recall that a square…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear algebra: please solve last 2 parts of question 3.3 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
24
(a) B=
(b) C =
2
[1
4 5
7
6 9 12 15
1
1
1 1
362
4
(c) D=
(d) E=
[12 -3 0
12 1 1
36 -5 1
4
1]
[1 1 1
12 0
7
6
13 -1 10
13
21
14 -2 20 23
0
15 3 35 0 126
16-4 56 55 252
1
4
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 7/2 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.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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