Let V and W be finite-dimensional vector spaces and T: V--> W be linear.

a) Prove that if dim(v)< dim(W), then T cannot be onto.

b) Prove that if dim(V)> dim(W), the T cannot be 1-1

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- Jul 5th 2008, 08:59 PMJCIRLinear Algebra help
Let V and W be finite-dimensional vector spaces and T: V--> W be linear.

a) Prove that if dim(v)< dim(W), then T cannot be onto.

b) Prove that if dim(V)> dim(W), the T cannot be 1-1 - Jul 6th 2008, 12:42 PMThePerfectHacker
Use rank-nullity theorem on $\displaystyle T$.