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Proof of kera = imb implies ima^t = kerb^t ask question asked 6 years ago modified 6 years ago

We actually got this example from the book, where it used projection on w to prove that dimensions of w + w perp are equal to n, but i don't think it mentioned orthogonal projection, though i could be wrong (maybe we are just assumed not to do any other projections at our level, or maybe it was assumed it was a perpendicular projection, which i guess is the same thing). Thank you arturo (and everyone else) I managed to work out this solution after completing the assigned readings actually, it makes sense and was pretty obvious Could you please comment on also, while i know that ker (a)=ker (rref (a)) for any matrix a, i am not sure if i can say that ker (rref (a) * rref (b))=ker (ab)