Question on: JAMB Mathematics - 2007
If f (x) = 3x - 2, P = \(\begin{pmatrix} 2 & 1 \ -1 & 0 \end{pmatrix}\) and I is 2 X 2 identity matrix, evaluate f(P)
A
\(\begin{pmatrix} 6 & 3 \ -3 & 0 \end{pmatrix}\)
B
\(\begin{pmatrix} 2 & 0 \ 0 & 2 \end{pmatrix}\)
C
\(\begin{pmatrix} 8 & 3 \ -3 & 2 \end{pmatrix}\)
D
\(\begin{pmatrix} 4 & 3 \ -3 & -2 \end{pmatrix}\)
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Correct Option: D
f(x) = 3x - 2, f(P) = 3p - 2I
= 3\(\begin{pmatrix} 2 & 1 \ -1 & 0 \end{pmatrix}\) - 2\(\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\) = \(\begin{pmatrix} 6 & 3 \ -3 & 0 \end{pmatrix}\) - \(\begin{pmatrix} 2 & 0 \ 0 & 2 \end{pmatrix}\)
= \(\begin{pmatrix} 6 & -2 \ -3 & 0 \end{pmatrix}\)\(\begin{pmatrix} 3 & -0 \ 0 & -2 \end{pmatrix}\) = \(\begin{pmatrix} 4 & 3 \ -3 & -2 \end{pmatrix}\)
= 3\(\begin{pmatrix} 2 & 1 \ -1 & 0 \end{pmatrix}\) - 2\(\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\) = \(\begin{pmatrix} 6 & 3 \ -3 & 0 \end{pmatrix}\) - \(\begin{pmatrix} 2 & 0 \ 0 & 2 \end{pmatrix}\)
= \(\begin{pmatrix} 6 & -2 \ -3 & 0 \end{pmatrix}\)\(\begin{pmatrix} 3 & -0 \ 0 & -2 \end{pmatrix}\) = \(\begin{pmatrix} 4 & 3 \ -3 & -2 \end{pmatrix}\)
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