Given $v=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $-{\frac{49}{6}}$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $-{\frac{29}{3}}$ $-{\frac{17}{3}}$

,

find the coordinates for $v$ in the subspace $W$ spanned by

$u_{1}=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ -4 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ -4 2

and $u_{2}=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 2 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 4 12

.

Note that $u_{1}$ and $u_{2}$ are orthogonal.

$v=$ $u_{1}+$ $u_{2}$