1. Find the matrix A of the linear transformation T from R2 to R2 that rotates any vector through an angle of 45∘ in the counterclockwise direction.2. To every linear transformation T from R2 to R2, there is an associated 2×2 matrix. Match the following linear transformations with their associated matrix. A = 1. Reflection about the y-axis2. Reflection about the x-axis3. Reflection about the line y3Dx4. Clockwise rotation by T/2 radians5. Counter-clockwise rotation by T/2 radians6. The projection onto the x-axis given by T(x,y)=(x,0)1A.0 -10 -111C.1|-111Е.11 0F.G. None of the aboveB.D.

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Answered: Find the matrix A of the linear…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 25E

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1. Find the matrix A of the linear transformation T from R² to R² that rotates any vector through an angle of 45^∘ in the counterclockwise direction.

2. To every linear transformation T from R² to R², there is an associated 2×2 matrix. Match the following linear transformations with their associated matrix.

1. Reflection about the y-axis
2. Reflection about the x-axis
3. Reflection about the line y3Dx
4. Clockwise rotation by T/2 radians
5. Counter-clockwise rotation by T/2 radians
6. The projection onto the x-axis given by T(x,y)=(x,0)
1
A.
0 -1
0 -1
1
1
C.
1
|
-1
1
1
Е.
1
1 0
F.
G. None of the above
B.
D.

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