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1) Let T:V->W be a linear transformation. Prove that T is one-to-one if and only if the rank of T equals the dimension of V.

1) Let T:V->W be a linear transformation. Prove that T is one-to-one if and only if the rank of T equals the dimension of V.

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Given T : V → W
We know that T is injective if and only if Ker(T ) = 0. that is T is injective
if and only if dim(Ker(T )) = 0 that is Nullity of T = 0. And we know by rank
nullity theorem that...

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