- #1
Hwng10
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Homework Statement
Let V and W be finite dimensional vector spaces.Given dim(V)≤ dim(W)
, prove that there exists a one-to-one linear transformation T : V -> W .
Homework Equations
The Attempt at a Solution
What I want to prove here is to show that nullity=0
dim(V) ≤ dim (W)
dim(N(T)) + dim(R(T)) ≤ dim(W)