Given matrix M = \(\begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix}\), find \(M^{T} + 2M\)

  • A \(\begin{vmatrix} -4 & 2 & 1\\ 6 & 0 & 5 \\ 0 & 6 & 2 \end{vmatrix}\)
  • B \(\begin{vmatrix} -6 & 0 & 13\\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)
  • C \(\begin{vmatrix} 5 & 2 & 6 \\ 0 & 1 & 1\\ 3 & 4 & -7 2 & 6 \end{vmatrix}\)
  • D \(\begin{vmatrix} -4 & 0 & 8 \\ 0 & -2 & -16 \\ 10 & 1 & 5 \end{vmatrix}\)
jamb 2019mathematics

The correct answer is B. \(\begin{vmatrix} -6 & 0 & 13\\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)

To find \(M^{T} + 2M\), first, find the transpose of matrix M (denoted as \(M^{T}\)):

\(M^{T} = \begin{vmatrix} -2 & 0 & 5 \\ 0 & -1 & 6 \\ 4 & 6 & 3 \end{vmatrix}\).

Next, multiply matrix M by 2:

\(2M = 2 \times \begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix} = \begin{vmatrix} -4 & 0 & 8 \\ 0 & -2 & 12 \\ 10 & 12 & 6 \end{vmatrix}\).

Finally, add the two matrices together:

\(M^{T} + 2M = \begin{vmatrix} -2 & 0 & 5 \\ 0 & -1 & 6 \\ 4 & 6 & 3 \end{vmatrix} + \begin{vmatrix} -4 & 0 & 8 \\ 0 & -2 & 12 \\ 10 & 12 & 6 \end{vmatrix} = \begin{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\).

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