You are given that T:U→X is a linear transformation. Prove that, T(c;u, + C2U2 + · = c, T(u1) + c2T(u2) + · · · + C„T(Un) for all u; e U and for all c, e Rand n2 1. ...+ Cnun)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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You are given that T:U→X is a linear transformation. Prove that, T(c;u, + C2U2 + ·
= c, T(u1) + c2T(u2) + · · · + C„T(Un) for all u; e U and for all c, e Rand n2 1.
+ Cnun)
Transcribed Image Text:You are given that T:U→X is a linear transformation. Prove that, T(c;u, + C2U2 + · = c, T(u1) + c2T(u2) + · · · + C„T(Un) for all u; e U and for all c, e Rand n2 1. + Cnun)
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