Prove that the zero transformation and the identity transformation are linear transformations.(a) the zero transformationLet V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V→ W be the zero transformation. Which of the following proves the zero transformlinear transformation? (Select all that apply.)Т(с + v) 3D с +0 %3D с + T(v)=T(vw)= 0= 0 : 0T(v) T(w)T(cvw) = 0 = c0 ·0 = cT(v) T(w)%3DT(cv)= 0 = c0 = cT(v)CT(v + w) = c(0 + 0) = cT(v) + cT(w)%3DT(v + w) = 0 = 0 + 0 =T(v) + T(w)(b) the identity transformationLet V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V → V be the identity transformation. Which of the following proves the identity transformlinear transformation? (Select all that apply.)T(cv) = cv =cT(v)T(vw)= VW =T(v) T(w)CT(v + w)c(v + w)CT(v) + cT(w)T(v + w) = v + w = T(v) + T(w)T(c + v) = c + v = c + T(v)T(cvw)= CVw =CT(v) T(w)

Prove that the zero transformation and the identity transformation are linear transformations. (a) the zero transformation Let V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V → W be the zero transformation. Which of the following proves the zero transform linear transformation? (Select all that apply.) O T(c + v) = c + 0 = c + T(v) O T(vw) = 0 = 0.0 = T(v) T(w) O T(cvw) = 0 = co · 0 = cT(v) T(w) O T(cv) = 0 = c0 = cT(v) O CT(v + w) = c(0 + 0) = cT(v) + cT(w) O T(v + w) = 0 = 0 +0 = T(v) + T(w) (b) the identity transformation Let V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V→ V be the identity transformation. Which of the following proves the identity transform linear transformation? (Select all that apply.) O T(cv) = cV = cT(v) O T(vw) = vw = T(v) T(w) O CT(v + w) = c(v + w) = cT(v) + cT(w) T(v + w) = v + w = T(v) + T(w) O T(c + v) = c + v = c + T(v) T(cvw) = cvw = cT(v) T(w)

Prove that the zero transformation and the identity transformation are linear transformations. (a) the zero transformation Let V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V → W be the zero transformation. Which of the following proves the zero transform linear transformation? (Select all that apply.) O T(c + v) = c + 0 = c + T(v) O T(vw) = 0 = 0.0 = T(v) T(w) O T(cvw) = 0 = co · 0 = cT(v) T(w) O T(cv) = 0 = c0 = cT(v) O CT(v + w) = c(0 + 0) = cT(v) + cT(w) O T(v + w) = 0 = 0 +0 = T(v) + T(w) (b) the identity transformation Let V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V→ V be the identity transformation. Which of the following proves the identity transform linear transformation? (Select all that apply.) O T(cv) = cV = cT(v) O T(vw) = vw = T(v) T(w) O CT(v + w) = c(v + w) = cT(v) + cT(w) T(v + w) = v + w = T(v) + T(w) O T(c + v) = c + v = c + T(v) T(cvw) = cvw = cT(v) T(w)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 67E: Guided Proof Let B be an invertible nn matrix. Prove that the linear transformation T:Mn,nMn,n...

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