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I'm solving this question, but I don't know what it is.

Consider a plane $x - y + z = 0$, and a point $b = (1, 2, 0)^T$

a) Find a basis of this plane, and a basis of orthogonal subspace to this plane.

b) Find the closest point $\hat{b}$ on the plane to b.

c) What is the error between b and $\hat{b}$?

Is this a linear algebra problem? What's a basis of orthogonal subspace and closest point $\hat{b}$? What's the error between b and $\hat{b}$??

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    «Is this a linear algebra problem?» is a new angle :)2010-10-26
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    sorry, I can't understand..2010-10-26
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    What Mariano means is that it's completely obvious that this is a linear algebra problem!2010-10-26
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    In what context did you come across this? It looks like a typical exercise in a linear algebra course. If you are indeed taking such a course, your textbook should explain in detail what the word "basis" means, and how to solve this problem. And then you should also have access to teachers that you can ask; this sort of thing is easier to explain face to face than in writing. By the way, the word "error" here simply means the distance between the points $b$ and $\hat{b}$.2010-10-26

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