If \(a = \begin{pmatrix} 3 \\ 2 \end{pmatrix}\) and \(b = \begin{pmatrix} -3 \\ 5
FURTHER MATHEMATICS
WAEC 2006
If \(a = \begin{pmatrix} 3 \\ 2 \end{pmatrix}\) and \(b = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\), find a vector c such that \(4a + 3c = b\).
- A. \(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\)
- B. \(\begin{pmatrix} -5 \\ -1 \end{pmatrix}\)
- C. \(\begin{pmatrix} -5 \\ 1 \end{pmatrix}\)
- D. \(\begin{pmatrix} -5 \\ -9 \end{pmatrix}\)
Correct Answer: B. \(\begin{pmatrix} -5 \\ -1 \end{pmatrix}\)
Explanation
\(4 \begin{pmatrix} 3 \\ 2 \end{pmatrix} + 3 \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\)
\(\begin{pmatrix} 12 \\ 8 \end{pmatrix} + \begin{pmatrix} 3x \\ 3y \end{pmatrix} = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\)
\(\begin{pmatrix} 3x \\ 3y \end{pmatrix} = \begin{pmatrix} -3 - 12 \\ 5 - 8 \end{pmatrix}\)
\(\begin{pmatrix} 3x \\ 3y \end{pmatrix} = \begin{pmatrix} -15 \\ -3 \end{pmatrix}\)
\(\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -5 \\ -1 \end{pmatrix}\)
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