Page 72 - Linear Algebra Done Right
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Chapter 3. Linear Maps
58
Now suppose (c) holds, so that T is surjective. Thus range T = V.
From 3.4 we have
dim null T = dim V − dim range T
= 0,
which implies that null T equals {0}. Thus T is injective (by 3.2), and
so T is invertible (we already knew that T was surjective). Hence (c)
implies (a), completing the proof.
