Let W = span $\displaystyle \[\left \{ \begin{bmatrix}

1\\

2\\

-1

\end{bmatrix}, \begin{bmatrix}

-1\\

3\\

2

\end{bmatrix} \right \}\]

$

Find a basis for the $\displaystyle \[W^{\perp }\]

$

I am really confused on how to find this.

So i turned it it a matrix and got the rref.

$\displaystyle \[\begin{bmatrix}

1 & -1\\

2 &3 \\

-1& 2

\end{bmatrix}\sim \begin{bmatrix}

1 & 0\\

0 & 1\\

0& 0

\end{bmatrix}\]

$

I must've did this wrong because the answer is $\displaystyle \[\begin{bmatrix}

7/5 \\

-1/5 \\

1

\end{bmatrix}\]

$

I understand how they got the 1, but I have no idea how they got 7/5 and -1/5.

Can someone please explain. Thanks in advance