Let W $=$ Span $($v$1,$ v$2)$ R$4$ and x be a vector in R$4,$ where

v$1=$

$$

$$

$$

$$

$1/2$

$1/2$

$1/2$

$1/2$

$$

$$

$$

$,$ v$2=$

$$

$$

$$

$$

$1/2$

$1/2$

$1/2$

$1/2$

$$

$$

$$

$,$ x $=$

$$

$$

$$

$$

$1$

$2$

$3$

$4$

$$

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$$

$$

$($a$)$ Show that $\{$v$1,$ v$2\}$ is an orthonormal basis for W $.$

$($b$)$ Compute projW $($x$).$

$($c$)$ Compute a basis for the orthogonal complement W $.$