Answered: Let T: R3-->R4 be a linear…

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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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