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You'll need to complete a few actions and gain 15 reputation points before being able to upvote 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). Upvoting indicates when questions and answers are useful

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What's reputation and how do i get it I thought that i can use any two linear independent vectors for this purpose, like $$ ima = \ { (1,0,0), (0,1,0 Instead, you can save this post to reference later.

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

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) Is this statement true? just out of my curiosity?

To gain full voting privileges, It is $$ kera = (1,1,1) $$ but how can i find the basis of the image What i have found so far is that i need to complement a basis of a kernel up to a basis of an original space But i do not have an idea of how to do this correctly