1. Show the function T : R² → R³ given by T(x, y) = (x − y, 3x + 2y, 0) is linear. Find the matrix A of T so that T ([]) = ₁ [] A
1. Show the function T : R² → R³ given by T(x, y) = (x − y, 3x + 2y, 0) is linear. Find the matrix A of T so that T ([]) = ₁ [] A
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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![### Linear Transformation Problem
**Problem Statement:**
1. Show the function \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^3 \) given by \( T(x, y) = (x - y, 3x + 2y, 0) \) is linear.
**Further Instructions:**
Find the matrix \( A \) of \( T \) so that
\[ T \left( \begin{bmatrix} x \\ y \end{bmatrix} \right) = A \begin{bmatrix} x \\ y \end{bmatrix}. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04829d0-4645-426e-bf1a-7ada40b0786f%2Fa7a0c502-b01e-42fb-9264-3164266ebe96%2Fkfgnqq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Transformation Problem
**Problem Statement:**
1. Show the function \( T : \mathbb{R}^2 \rightarrow \mathbb{R}^3 \) given by \( T(x, y) = (x - y, 3x + 2y, 0) \) is linear.
**Further Instructions:**
Find the matrix \( A \) of \( T \) so that
\[ T \left( \begin{bmatrix} x \\ y \end{bmatrix} \right) = A \begin{bmatrix} x \\ y \end{bmatrix}. \]
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