How do you find the best approximation in linear algebra?

Question

Find the best approximation to a solution of the following system:?
{2x-y=1}
{x+3y=0}
{3x+2y=2}

I reduced the matrix to:
{x + 0y = 3/7}
{0x + y = -1/7}
{0x + 0y = 1}

I just don't know how to find the best approximation. In my text book it says to calculate ||e||=||b-Ax|| where e is the error value but I'm not sure what values to plug in to get the correct answer.

nordo360 · Accepted Answer

this is 311! i just finished this problem: check out example example 1 in section 5.6 of the textbook (page 267) this example is almost exactly the same. you will need to use the normal equations for Z. The most difficult part will be finding the inverse of the the invertible matrix A(transpose)A, and this is not difficult at all. good luck!

Anonymous · Answer

Not really an answer but thank you for asking it im actually doing the same thing right now aha i dont really understand 311 very well at all

hockenberry · Answer

Say you have a vector section V, with a subset S. S is a subspace if and offered that: a million. given vectors p and q in W, p + q is likewise in W. 2. given vector p and scalar c, cp is likewise in W. those are the closure residences you like. want this replace into what you have been searching for.

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How do you find the best approximation in linear algebra?

3 Answers