p = (24)\begin{pmatrix}2 \\ 4\end{pmatrix}(24) and q = (10−1)\begin{pmatrix}10 \\ -1\end{pmatrix}(10−1), r = (xy)\begin{pmatrix}x \\ y\end{pmatrix}(xy)
2p - 3r = q
2( (24)\begin{pmatrix}2 \\ 4\end{pmatrix}(24)) - 3( (xy)\begin{pmatrix}x \\ y\end{pmatrix}(xy)) = (10−1)\begin{pmatrix}10 \\ -1\end{pmatrix}(10−1)
[(48)\begin{pmatrix}4 \\ 8\end{pmatrix}(48) - (3x3y)\begin{pmatrix}3x \\ 3y\end{pmatrix}(3x3y)] = (10−1)\begin{pmatrix}10 \\ -1\end{pmatrix}(10−1)
4 - 3x = 10, then, -3x = 6, so that, x = -2,
8 - 3y = -1, then, -3y = -9, so that, y = 3
Thus, r = (−23)\begin{pmatrix}-2 \\ 3\end{pmatrix}(−23)