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## Homework Statement

Let V = Gen{ [0;5;1;2], [4;0;-2;1], [5,1,0,1]}. Define u1

_{1}=v

_{1}. Indicate the coordinates of u

_{2}, the orthogonal component of v

_{2}to V

_{1}=Gen{u

_{1}.

## Homework Equations

I know V has to be a vector space. If there is a subspace W with an orthogonal basis B={v

_{1},...,v

_{k}} then the orthogonal component of any vector u to W is

u

_{c}=u - (<u,v

_{1}>/<v

_{1},v

_{1}>)*v

_{1}- ... - (<u,v

_{k}>/<v

_{k},v

_{k}>)*v

_{k}

## The Attempt at a Solution

I don-t even know where to start since the basis given is not orthogonal. Do I have to construct an orthogonal basis from the three vectors given and then proceed to solve it? I didn't see this topic in class so I didn't see the professor do this, I'm doing this for extra credit on the subject. Anyone knows where I could find a worked out example of this type of problems? Thank you.