Chapter 3.9, Problem 7E

Exercise $1-16$ refers to the following subspaces:

$c)$ $W=R\left(B\right)$, $B=\left[\begin{array}{ccc}1& 2& 4\\ -1& 0& -2\\ 1& 1& 3\end{array}\right]$

In Exercises $1-10$, find a basis for the indicated subspace $W$. For the given vector $v$, solve the normal equations $\left(2\right)$ and determine the best approximation $w^{*}$. Verify that $v-w^{*}$ is orthogonal to the basis vectors.

$W$ given by $\left(b\right)$, $v={\left[2,0,4\right]}^T$