Suppose that T : R' → R' is a linear transformation whose standard matrix has 2 pivots. Is it possible to find two different vectors u, v such that T(u) =T(v)? That is, is (i) T one-to-one? Answer and explain briefly how you know. (ii) Given any vector b in R2, is it possible to find x such that T(x) = b? That is, does T map onto R?. Answer and explain briefly how you know.

Suppose that T : R' → R' is a linear transformation whose standard matrix has 2 pivots. Is it possible to find two different vectors u, v such that T(u) =T(v)? That is, is (i) T one-to-one? Answer and explain briefly how you know. (ii) Given any vector b in R2, is it possible to find x such that T(x) = b? That is, does T map onto R?. Answer and explain briefly how you know.

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 11CM

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