Consider the coordinate vectors
\begin{bmatrix} 7 \\ -2 \\ 4 \end{bmatrix}, \begin{bmatrix} 3 \\ 0 \\ 4 \end{bmatrix}, \begin{bmatrix} -10 \\ 7 \\ 5 \\ 2 \end{bmatrix}
(a) Find $w$ if $S$ is the basis in \{ (3, 1, -4), (2, 5, 6), (1, 4, 8) \}.
$w = (?, ?, ?)$
(b) Find $q$ if $S$ is the basis in $x^2 + 1$, $x^2 - 1$, $2x - 1$.
$q = $
(c) Find $B$ if $S$ is the basis in $\begin{bmatrix} 3\\ 3 \end{bmatrix}$, $\begin{bmatrix} 6\\ -6 \end{bmatrix}$, $\begin{bmatrix} 0\\ -1 \end{bmatrix}$, $\begin{bmatrix} -1\\ 0 \end{bmatrix}$, $\begin{bmatrix} 0\\ -12 \end{bmatrix}$, $\begin{bmatrix} -8\\ -4 \end{bmatrix}$,
$\begin{bmatrix} 1\\ -1 \end{bmatrix}$, $\begin{bmatrix} 0\\ 2 \end{bmatrix}$
$B = \begin{pmatrix} ? & ? & ?\\ ? & ? & ? \end{pmatrix}$
