If p = \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\) and q = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\), find a vector, r such that 2p – 3r = q
-
\(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)
- \(\begin{pmatrix} -26 \\ 11 \end{pmatrix}\)
- \(\begin{pmatrix} 2 \\ 3 \end{pmatrix}\)
- \(\begin{pmatrix} 6 \\ -9 \end{pmatrix}\)
The correct answer is: A
Explanation
p = \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\) and q = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\), r = \(\begin{pmatrix} x \\ y \end{pmatrix}\)
2p - 3r = q
2( \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\)) - 3( \(\begin{pmatrix} x \\ y \end{pmatrix}\)) = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\)
[\(\begin{pmatrix} 4 \\ 8 \end{pmatrix}\) - \(\begin{pmatrix} 3x \\ 3y \end{pmatrix}\)] = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\)
4 - 3x = 10, then, -3x = 6, so that, x = -2,
8 - 3y = -1, then, -3y = -9, so that, y = 3
Thus, r = \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)