Answer
Yes.
Work Step by Step
We know that the determinant of a matrix \[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
is $D=ad-bc$.
We know that if we choose $2$ of these vectors and the determinant of the matrix formed by the vectors is not $0$, then they span the plane. If we choose $(1,-1),(2,3)$, then $D=1\cdot3-(-1)2=3+2=5\ne0$.
