The Vector X Is in a Subspace H with a Basis

Multiple Choice

The vector x is in a subspace H with a basis β = {b₁, b₂}. Find the β-coordinate vector of x.

- $$\mathbf { b } _ { 1 } = \left[ \begin{array} { r } 1 \\- 2\end{array} \right] , \mathbf { b } _ { 2 } = \left[ \begin{array} { r } - 5 \\3\end{array} \right] , \mathbf { x } = \left[ \begin{array} { r } 22 \\- 16\end{array} \right]$$

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

B) $\left[\begin{array}{r}-2 \\ 4\end{array}\right]$

C) $\left[\begin{array}{r}2 \\ -4\end{array}\right]$

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