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# a. Prove that if T : Rn Rm is a linear transformation and c is any scalar, then the

ISBN: 9781429215213 438

## Solution for problem 11 Chapter 2.2

Linear Algebra: A Geometric Approach | 2nd Edition

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Linear Algebra: A Geometric Approach | 2nd Edition

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Problem 11

a. Prove that if T : Rn Rm is a linear transformation and c is any scalar, then the function cT : Rn Rm defined by (cT )(x) = cT (x) (i.e., the scalar c times the vector T (x)) is also a linear transformation. b. Prove that if S : Rn Rm and T : Rn Rm are linear transformations, then the function S + T : Rn Rm defined by (S + T )(x) = S(x) + T (x) is also a linear transformation. c. Prove that if S : Rm Rp and T : Rn Rm are linear transformations, then the function ST : Rn Rp is also a linear transformation.

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Fall 2011 MA 16200 Study Guide - Exam # 1 ▯ (1) Distance formula D = (x2− x 1 + (y −2y ) 1 (z − 2 ) ;1equation of a sphere with cen- 2 2 2 2 ter (h,k,l) and radius r: (x − h) + (y − k) + (z − l) = r . −→ (2) Vectors in R and R ; displacement...

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##### ISBN: 9781429215213

The full step-by-step solution to problem: 11 from chapter: 2.2 was answered by , our top Math solution expert on 03/15/18, 05:30PM. This textbook survival guide was created for the textbook: Linear Algebra: A Geometric Approach, edition: 2. The answer to “a. Prove that if T : Rn Rm is a linear transformation and c is any scalar, then the function cT : Rn Rm defined by (cT )(x) = cT (x) (i.e., the scalar c times the vector T (x)) is also a linear transformation. b. Prove that if S : Rn Rm and T : Rn Rm are linear transformations, then the function S + T : Rn Rm defined by (S + T )(x) = S(x) + T (x) is also a linear transformation. c. Prove that if S : Rm Rp and T : Rn Rm are linear transformations, then the function ST : Rn Rp is also a linear transformation.” is broken down into a number of easy to follow steps, and 114 words. Linear Algebra: A Geometric Approach was written by and is associated to the ISBN: 9781429215213. Since the solution to 11 from 2.2 chapter was answered, more than 212 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 31 chapters, and 547 solutions.

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