Hey people. I find myself getting through my course but currently with not as much understanding as I would like. We've got to some proofs and i either vaguely understand them or do not know how to prove them.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

The first would be to prove the Dimension theorem that.

dimU + dimV = dim(U + V) + dim( U intersection V )

The second is if U,V are finite dimensional vector spaces over a field, and T: V -> W is a bijection

Show dimU = dimW

The last is to do with the Rank-Nullity Theorem and a basic linear transformation T: Rn -> Rm

That if m < n prove that T is not injective

And if m = n prove that T is injective iff T is surjective.

Some general insight into these proofs would be very very helpful. All feedback would be very much appreciated.

Thanks.

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# Linear Algebra Proofs.

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