Linear Algebra Problem 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 transformation from V to W is a lineartransformation? (Select all that apply.)O T(cvw) = 0 = co · 0 = cT(v) T(w)V T(c + v) = c + 0 = c + T(v)VT(vw) = 0 = 0· 0 = T(v) T(w)V T(v + w) = 0 = 0 + 0 = T(v) + T(w)V T(cv) = 0 = c0 = cT(v)M cT(v + w) = c(0 + 0) = cT(v) +CT(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 transformation from V to V is a lineartransformation? (Select all that apply.)V T(cv) = cv = cT(v)V T(cvw) = cvw = cT(v) T(w)M cT(v + w) = c(v + w) = cT(v) +cT(w)V T(v + w) = v + w = T(v) + T(w)V T(vw) = vw = T(v) T(w)V T(c + v) = c + v = c + T(v)

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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 transformation from transformation? (Select all that apply.) O T(cvw) = 0 = c0 · 0 = cT(v) T(w) O T(c + v) = c + 0 = c + T(v) T(vw) = 0 = 0.0 - T(v) T(w) O T(v + w) = 0 = 0 + 0 = T(v) + T(w) O T(cv) = 0 = c0 = cT(v) n CT(v + w) = c(0 + 0) = cT(v) + CT(w) 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 transformation from transformation? (Select all that apply.) O T(cv) = cv = cT(v) O T(cvw) = cvw - cT(v) T(w) - cT(v + w) - c(v + w) = cT(v) + CT(w) O T(v + w) - v + w - T(v) + T(w) O T(vw) = vw = T(v) T(w) O T(c + v) -c + v = c + T(v)

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 transformation from transformation? (Select all that apply.) O T(cvw) = 0 = c0 · 0 = cT(v) T(w) O T(c + v) = c + 0 = c + T(v) T(vw) = 0 = 0.0 - T(v) T(w) O T(v + w) = 0 = 0 + 0 = T(v) + T(w) O T(cv) = 0 = c0 = cT(v) n CT(v + w) = c(0 + 0) = cT(v) + CT(w) 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 transformation from transformation? (Select all that apply.) O T(cv) = cv = cT(v) O T(cvw) = cvw - cT(v) T(w) - cT(v + w) - c(v + w) = cT(v) + CT(w) O T(v + w) - v + w - T(v) + T(w) O T(vw) = vw = T(v) T(w) O T(c + v) -c + v = c + T(v)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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