Let T: Rm R and S: R RP be linear transformations. Then So T: Rm RP is a linear transformation. Moreover, their standard matrices are related by [So T] = [S][T]. Verify the theorem above by finding the matrix of S o T by direct substitution and by matrix multiplication of [S][T]. Y₁ +4Y₂ CHRICE*] = 2y₁ + y2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
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Let T: Rm R and S: R RP be linear transformations. Then So T: Rm RP is a linear transformation. Moreover, their standard matrices are related by
[So T] = [S][T].
Verify the theorem above by finding the matrix of S o T by direct substitution and by matrix multiplication of [S][T].
+4₂
Q-R}X-***]
+ y2
(a) by direct substitution
(b) by matrix multiplication
Transcribed Image Text:Let T: Rm R and S: R RP be linear transformations. Then So T: Rm RP is a linear transformation. Moreover, their standard matrices are related by [So T] = [S][T]. Verify the theorem above by finding the matrix of S o T by direct substitution and by matrix multiplication of [S][T]. +4₂ Q-R}X-***] + y2 (a) by direct substitution (b) by matrix multiplication
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