# Linear Algebra - Orthogonal Bases

Please see the attached file for the fully formatted problems.

Let V = Span ((1, -1, 0, 2), (1, 0, 1, 1)) C R^4, and let b = (1, -3, 1, 1).

a. Find an orthogonal basis for V.

b. Use your answer to a to find p = proj_v b.

c. Letting

A = [ 1 1

-1 0

0 1

2 1]

user your answer to b to give the least squares solution of Ax - b.

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#### Solution Summary

Orthogonal bases are investigated in this solution, which is given by step by step equations in an attached Word document.

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