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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. \(\begin{pmatrix} -5 \\ -9 \end{pmatrix}\)
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Correct Answer: Option B
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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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
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