If P = \(\begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatrix}\) , what is...

Mathematics

JAMB 2010

If P = \(\begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatrix}\) , what is P\(^-1\)

A. \(\begin{pmatrix} -{\frac{1}{5}} & -{\frac{3}{5}} \\ -{\frac{1}{5}} & -{\frac{2}{5}} \end{pmatrix}\)
B. \(\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ {\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}\)
C. \(\begin{pmatrix} -{\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}\)
D. \(\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}\)

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Correct Answer: Option D

Explanation

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

|P| = 2 - 1 x -3 = 5

P-1 = \(\frac{1}{5}\)\(\begin{pmatrix} 1 & 3 \\ -1 & 2 \end{pmatrix}\)

= \(\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}\)

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