Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. T(A) = A6 from R6x6 to R6x6 T(A) = trace(A) from R4x4 to R -8 T(4) = A [ 1 2 ³] - [18] 9 T(A) = ASA-¹ from R²x2 to R²x2, where S = -4 7 T(A) = A [ ²2 1] som R to R² from 3 T(A) = 4A from R6x3 to R6x3 A from R²x2 to R2x2 [4] [23²2 8 -6
Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. T(A) = A6 from R6x6 to R6x6 T(A) = trace(A) from R4x4 to R -8 T(4) = A [ 1 2 ³] - [18] 9 T(A) = ASA-¹ from R²x2 to R²x2, where S = -4 7 T(A) = A [ ²2 1] som R to R² from 3 T(A) = 4A from R6x3 to R6x3 A from R²x2 to R2x2 [4] [23²2 8 -6
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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Question
![Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers.
] A. T(A) = A6 from R6×6 to R6×6
|B. T(A) = trace(A) from R4×4 to R
1[10 2]-[18]
6
6 9
c. T(A) = A
D. T(A) = ASA-¹ from R²×² to R²×², where S
=
}]
3
E. T(A) = A
= A[
2
6x3
OF. T(A) = 4A from R6׳ to R6׳
R6x3
2x2
A from R2×2 to R²×2
-4 7
2x2
from R to R²X2
-2
8
46]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ff93d80-f747-4f15-803d-56788ff3d116%2F95d4e6a7-828e-4447-a0cc-cca837295a43%2Fnsf1b4f_processed.png&w=3840&q=75)
Transcribed Image Text:Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers.
] A. T(A) = A6 from R6×6 to R6×6
|B. T(A) = trace(A) from R4×4 to R
1[10 2]-[18]
6
6 9
c. T(A) = A
D. T(A) = ASA-¹ from R²×² to R²×², where S
=
}]
3
E. T(A) = A
= A[
2
6x3
OF. T(A) = 4A from R6׳ to R6׳
R6x3
2x2
A from R2×2 to R²×2
-4 7
2x2
from R to R²X2
-2
8
46]
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