Question 15 of 28
Consider the coordinate vectors
\begin{bmatrix} 7 \ -2 \ 2 \end{bmatrix}, \begin{bmatrix} 6 \ 1 \ 4 \end{bmatrix}, \begin{bmatrix} -8 \ 7 \ 5 \ 1 \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 $\begin{bmatrix} 3 & 6 \ -6 & -1 \end{bmatrix}$, $\begin{bmatrix} 0 & -1 \ -1 & 0 \end{bmatrix}$, $\begin{bmatrix} 0 & -8 \ -12 & -4 \end{bmatrix}$,
$\begin{bmatrix} 1 & 0 \ -1 & 2 \end{bmatrix}$.
B = (, )
