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Prove that the transformation T: R 2 R 2 defined by T(x, y) = (2x, x + 3y) is linear

Linear Algebra with Applications | 8th Edition | ISBN: 9781449679545 | Authors: Gareth Williams ISBN: 9781449679545 435

Solution for problem 40 Chapter 4

Linear Algebra with Applications | 8th Edition

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Linear Algebra with Applications | 8th Edition | ISBN: 9781449679545 | Authors: Gareth Williams

Linear Algebra with Applications | 8th Edition

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Problem 40

Prove that the transformation T: R 2 R 2 defined by T(x, y) = (2x, x + 3y) is linear. Find the image of the vector { 1, 2) under this transformation.

Step-by-Step Solution:
Step 1 of 3

1.1 Systems of Linear Equations Linear equation – equation written in the form “a x +a x +…+a x =b” where 1 1 2 2 n n b & coefficients a 1…,a nre real or complex numbers, usually known in advance System of Linear Equations (linear system) – a collection of one or more linear equations involving the same variables Solution – a list (1 2s ,…,n ) of numbers that makes each equation a true statement when the values s …s 1re nubstituted for x x , r1…pentively Solution set – set of all possible solutions -Equivalent systems have the same solution set A system of linear equations has: 1. No solution (inconsistent system) 2. Exactly one solution (consistent system) 3. Infinitely many solutions (consistent system) Matri

Step 2 of 3

Chapter 4, Problem 40 is Solved
Step 3 of 3

Textbook: Linear Algebra with Applications
Edition: 8
Author: Gareth Williams
ISBN: 9781449679545

The answer to “Prove that the transformation T: R 2 R 2 defined by T(x, y) = (2x, x + 3y) is linear. Find the image of the vector { 1, 2) under this transformation.” is broken down into a number of easy to follow steps, and 32 words. Linear Algebra with Applications was written by and is associated to the ISBN: 9781449679545. Since the solution to 40 from 4 chapter was answered, more than 228 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 8. The full step-by-step solution to problem: 40 from chapter: 4 was answered by , our top Math solution expert on 03/15/18, 05:22PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 56 chapters, and 1286 solutions.

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Prove that the transformation T: R 2 R 2 defined by T(x, y) = (2x, x + 3y) is linear