Let f:ℝ→ℝ^3 be defined by f(x)=⟨6x,−4x,−4x⟩⟩. Is f a linear transformation? (a) f(x+y)=f(x+y)=(?) . f(x)+f(y)= (?)+(?) Does f(x+y)=f(x)+f(y) for all x,y∈ℝ? (b) f(cx)=(?) . c(f(x))= (?)((?)) Does f(cx)=c(f(x)) for all c,x∈

Let f:ℝ→ℝ^3 be defined by f(x)=⟨6x,−4x,−4x⟩⟩. Is f a linear transformation? (a) f(x+y)=f(x+y)=(?) . f(x)+f(y)= (?)+(?) Does f(x+y)=f(x)+f(y) for all x,y∈ℝ? (b) f(cx)=(?) . c(f(x))= (?)((?)) Does f(cx)=c(f(x)) for all c,x∈

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...

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Question

Let f:ℝ→ℝ^3 be defined by f(x)=⟨6x,−4x,−4x⟩⟩. Is f a linear transformation?

(a) f(x+y)=f(x+y)=(?) . f(x)+f(y)= (?)+(?)

Does f(x+y)=f(x)+f(y) for all x,y∈ℝ?

(b) f(cx)=(?) . c(f(x))= (?)((?))

Does f(cx)=c(f(x)) for all c,x∈ℝ?

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