Surjective linear transformations | Mathematics | Page 1

karmic dome Oct 23, 2023, 4:24 AM

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Need help with this problem..not really sure what to do.

Any help would be appreciated for either part a) or part b).

pulsar wolfBOT Oct 23, 2023, 4:24 AM

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shell pike Oct 23, 2023, 4:29 AM

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For (a), backwards direction, if $\dim(V) \geq \dim(W)$, you try to make a basis for both $V$ and $W$
say $V = {v_1, \dots, v_n}$ and ...

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Then you construct a simple linear transformation $T: V \to W$ that maps each basis element in $V$ to basis element in $W$

potent folioBOT Oct 23, 2023, 4:31 AM

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Dee3Cay

shell pike Oct 23, 2023, 4:33 AM

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in (a) you may also try proof by contradiction
(b) again you'll have to first suppose $V$ has basis ${v_1, \dots, v_n}$ and $W$ has basis...
Rule of thumb: you see finite-dimensional vector space, you may create a finite basis for that space

potent folioBOT Oct 23, 2023, 4:33 AM

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Dee3Cay

karmic dome Oct 26, 2023, 12:12 AM

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.solved

#Surjective linear transformations