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If f(x) = 3x - 2I, P = \(\begin{pmatrix}2 & 1 \\-1 & 0 \end{pmatrix}\) and I is 2 x 2...

Mathematics
JAMB 2007

If f(x) = 3x - 2I, 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 Answer: Option D
Explanation

I = \(\begin{pmatrix}1 & 0 \\0 & 1 \end{pmatrix}\)

Then, 3x - 2I becomes 3p - 2I (since we are finding f(p))

3\(\begin{pmatrix}2 & 1 \\-1 & 0 \end{pmatrix}\) - 2\(\begin{pmatrix}1 & 0 \\ 0 & 1 \end{pmatrix}\)

= \(\begin{pmatrix}6 & 3 \\-3 & 0 \end{pmatrix}\) - \(\begin{pmatrix}2 & 0 \\ 0 & 2 \end{pmatrix}\)

= \(\begin{pmatrix}4 & 3 \\-3 & -2 \end{pmatrix}\)

There is an explanation video available below.


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Explanation Video

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