Let T: R3-->R4 be a linear transformation such that the only solution to T(x)=0 is the trivial solution. a. Is T one-to-one? b.Does T map R3 onto R4? Justify your answer in each case.
Let T: R3-->R4 be a linear transformation such that the only solution to T(x)=0 is the trivial solution. a. Is T one-to-one? b.Does T map R3 onto R4? Justify your answer in each case.
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 4CM
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Let T: R3-->R4 be a linear transformation such that the only solution to T(x)=0 is the trivial solution.
a. Is T one-to-one?
b.Does T map R3 onto R4?
Justify your answer in each case.
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