Correct Answer: Option 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 = \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)

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