[Math] Find $x$ in $\mathbb{R}^2$ whose cordinate vector relative to the basis $B$

Question

Consider the basis $B$ of $\mathbb{R}^2$ consisting of vectors $\begin{bmatrix}5\\-1\end{bmatrix}$ and $\begin{bmatrix}-7\\-4\end{bmatrix}$. Find $x$ in $\mathbb{R}^2$ whose coordinate vector relative to the basis $B$ is $[x]_B = \begin{bmatrix}2\\5\end{bmatrix}$

$x = ?$

I put the matrices together obtaining a $3 \times 3$ matrix that I row reduced to get $\begin{bmatrix}1&0&-1\\0&1&-7/11\end{bmatrix}$ but then when I tried $x = \begin{bmatrix}-1\\-7/11\end{bmatrix}$ it said it was incorrect. I'm confused what i'm doing wrong

Answer 1

Hint:

Simply, your vector is: $$ 2 \begin{bmatrix} 5\\-1 \end{bmatrix} +5\begin{bmatrix} -7\\-4 \end{bmatrix} $$