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Linear Algebra

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Moderate

Closest vector in a subspace

LINALG-E1WXNZ

What is the closest vector in the column space of:

$$A = \begin{pmatrix} 1/\sqrt{2} & 1/\sqrt{3} \\\ 1/\sqrt{2} & -1/\sqrt{3} \\\ 0 & 1/\sqrt{3} \end{pmatrix} $$

...to the vector $\mathbf{v} = (1,2,0)$?

A

$(0,1,0)$

B

$(11/6,7/6,-1/3)$

C

$(1/\sqrt{5},2/\sqrt{5},0)$

D

(7/6,11/6,-1/3)

E

$(0,1,1)$