A =21O-1-2C=21-1-2[0.5 0.0]0.0 2.0-2 -10-2NOCe₁-1Ae₂Ce₂Ae₁0 10 122B =210-1-2D=21-1-2ALAS-24[0.5 0.5][0.5 0.5]-22210.433 0.250-0.250 0.433]Be₂0Be₁1De₂De122E =2-1-2-2劃[0.866 -0.500]0.500 0.866Ee₂Ee₁-1 0 1 2 Determine if the matrix does any of the following:A rotation• A projection• A reflection• Preserves the shape of the unit square• Preserves the area of the unit square

From the graphical structures, we determine the type of matrices.

Answered: Determine if the matrix does any of the…

Determine if the matrix does any of the following: • A rotation • A projection • A reflection • Preserves the shape of the unit square • Preserves the area of the unit square

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 37EQ

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Question

A =
2
1
O
-1
-2
C=
2
1
-1
-2
[0.5 0.0]
0.0 2.0
-2 -1
0
-2
NO
Ce₁
-1
Ae₂
Ce₂
Ae₁
0 1
0 1
2
2
B =
2
1
0
-1
-2
D=
2
1
-1
-2
ALAS
-2
4
[0.5 0.5]
[0.5 0.5]
-2
22
1
0.433 0.250
-0.250 0.433]
Be₂
0
Be₁
1
De₂
De
1
2
2
E =
2
-1
-2
-2
劃
[0.866 -0.500]
0.500 0.866
Ee₂
Ee₁
-1 0 1 2

Determine if the matrix does any of the following:
A rotation
• A projection
• A reflection
• Preserves the shape of the unit square
• Preserves the area of the unit square

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