Find the Specified Change-Of-Coordinates Matrix $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$

Multiple Choice

Find the specified change-of-coordinates matrix.
-Consider two bases $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$ and $C = \left\{ \mathbf { c } _ { 1 } , \mathbf { c } _ { 2 } \right\}$ for a vector space $V$ such that $\mathbf { b } _ { 1 } = \mathbf { c } _ { 1 } - 5 \mathbf { c } _ { 2 }$ and $\mathbf { b } _ { 2 } = 2 \mathbf { c } _ { 1 } - 4 c _ { 2 }$ . Find the change-of-coordinates matrix from $B$ to $C$ .

A)
$\left[ \begin{array} { r r } 1 & 2 \\ - 5 & - 4 \end{array} \right]$

B)

$\left[ \begin{array} { l l } 1 & - 5 \\ 2 & - 4 \end{array} \right]$

C)
$\left[ \begin{array} { l l } 1 & 2 \\ 5 & 4 \end{array} \right]$

D)
$\left[ \begin{array} { r r } 0 & 2 \\ - 5 & - 4 \end{array} \right]$