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Determine which of the following transformations are linear transformations. A. The transformation T defined by T(1, 2, 3) = (x1,0, x3) 3) = (x₁, x2, -X3) B. The transformation C. The transformation T defined by T(1, 2, T defined by T(x₁, x2, 3) = (1, X2, X3) D. The transformation T defined by T(x₁, x2) = (2x1 - 3x2,1 +4,5x2). E. The transformation T defined by T(x₁, x₂) = (4x₁2x2,3|x₂|).

Determine which of the following transformations are linear transformations. A. The transformation T defined by T(1, 2, 3) = (x1,0, x3) 3) = (x₁, x2, -X3) B. The transformation C. The transformation T defined by T(1, 2, T defined by T(x₁, x2, 3) = (1, X2, X3) D. The transformation T defined by T(x₁, x2) = (2x1 - 3x2,1 +4,5x2). E. The transformation T defined by T(x₁, x₂) = (4x₁2x2,3|x₂|).

Advanced Engineering Mathematics
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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Determine which of the following transformations are linear transformations. A. The transformation T defined by T(1, 2, X3) = (x1,0, X3) B. The transformation T defined by T(x1, x2, 3) = (x1, x2, -3) C. The transformation T defined by T(1, 2, 3) = (1, 2, 3) D. The transformation T defined by T(x₁, x2) = (2x1 - 3x2, x1 +4,5x₂). E. The transformation T defined by T(x₁, x2) = (4x₁ − 2x2, 3|x₂|). -
Transcribed Image Text:Determine which of the following transformations are linear transformations. A. The transformation T defined by T(1, 2, X3) = (x1,0, X3) B. The transformation T defined by T(x1, x2, 3) = (x1, x2, -3) C. The transformation T defined by T(1, 2, 3) = (1, 2, 3) D. The transformation T defined by T(x₁, x2) = (2x1 - 3x2, x1 +4,5x₂). E. The transformation T defined by T(x₁, x2) = (4x₁ − 2x2, 3|x₂|). -
Expert Solution
Step 1

We have been given transformations:

A. The transformation T is defined by Tx1, x2, x3=x1, 0, x3.

B. The transformation T is defined by Tx1, x2, x3=x1, x2, -x3.

C. The transformation T is defined by Tx1, x2, x3=1, x2, x3.

D. The transformation T is defined by Tx1, x2=2x1-3x2, x1+4, 5x2.

E. The transformation T is defined by Tx1, x2=4x1-2x2, 3x2.

We have to determine which of the given transformations are linear transformation.

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