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) AT from R4x6 to R6x4 B. T(A) - SAS-¹ from R²×² to R²×², where S = = = c. T(A) = det(A) from R6×6 to R D. T(A) = trace(A) from R5×5 to R E.T(A) A + I4 from R4×4 to R4×4 4 F. T(A) = = 3] -6 7 A from R2×4 to R²×4 9 -30

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 43E
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show step by step explanation of why some are linear transformations and the others are not 

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.
Ā. T(A) = AT from R4>
4x6
=
B. T(A) = SAS-¹ from R²×² to R²×2, where S
2x2
=
c. T(A)
D. T(A)
det(A) from R6×6 to R
trace(A) from R5×5 to R
E. T(A) = A + №₁ from R4×4 to R4×4
=
-
F. T(A) =
=
to R6x4
[46
3]
A from R2×4 to R²×4
9
[23
1
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. Ā. T(A) = AT from R4> 4x6 = B. T(A) = SAS-¹ from R²×² to R²×2, where S 2x2 = c. T(A) D. T(A) det(A) from R6×6 to R trace(A) from R5×5 to R E. T(A) = A + №₁ from R4×4 to R4×4 = - F. T(A) = = to R6x4 [46 3] A from R2×4 to R²×4 9 [23 1
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