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**1. Homework Statement**

In R

^{4}, let U = span((1, 1, 0, 0), (1, 1, 1, 2)). Find u in U such that ||u - (1, 2, 3, 4)|| is as small as possible.

**2. Homework Equations**

**3. The Attempt at a Solution**

I came up with a vector u = (-.5, -.5, 0, 0) + (2, 2, 2, 4) = (1.5, 1.5, 2, 4). Then u - (1, 2, 3, 4) = (0.5, -0.5, -1, 0). Using the standard dot product as the norm, I get ||(0.5, -0.5, -1, 0)|| = sqrt(.25 + .25 + 1) = sqrt(1.5).

This was probably a bad approach, but I can't think of any other real way to do this. Is this the right answer at least? If not, how could I approach this in a better manner other than just randomly picking vectors? Thanks.