If \(\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix} \), find x.

  • A 5
  • B 6
  • C 7
  • D 8
waec 2011furthermathematics

The correct answer is A. 5

\(\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix}\)

\(\begin{pmatrix} 3 \times 2 + 2 \times 3 \\ 7 \times 2 + x \times 3 \end{pmatrix} = \begin{pmatrix} 12 \\ 29 \end{pmatrix}\)

\(\implies 14 + 3x = 29 \)

\(3x = 29 - 14 = 15\)

\(x = 5\)

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