Question 26

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Jambmaths question: 

The inverse of matrix N =$\left( \begin{matrix}   2 & 3  \\   1 & 4  \\\end{matrix} \right)$ is

Option A: 

$\frac{1}{5}\left( \begin{matrix}   2 & -1  \\   -3 & 4  \\\end{matrix} \right)$

Option B: 

$\frac{1}{5}\left( \begin{matrix}   4 & 3  \\   -1 & 2  \\\end{matrix} \right)$

Option C: 

$\frac{1}{5}\left( \begin{matrix}   4 & -3  \\   -1 & 2  \\\end{matrix} \right)$

Option D: 

$\frac{1}{5}\left( \begin{matrix}   2 & 1  \\   3 & 4  \\\end{matrix} \right)$

Jamb Maths Solution: 

$\begin{align}  & \text{For a given 2}\times \text{2 matrix}\,A=\left( \begin{matrix}   a & b  \\   c & d  \\\end{matrix} \right) \\ & the\text{ }inverse\text{ }{{A}^{}}^{1}is\text{ }given\text{ }as \\ & {{A}^{-1}}=\left( \begin{matrix}   d & -b  \\   -c & a  \\\end{matrix} \right) \\ & \therefore N=\left( \begin{matrix}   2 & 3  \\   1 & 4  \\\end{matrix} \right) \\ & {{N}^{-1}}=\frac{1}{8-3}\left( \begin{matrix}   4 & -3  \\   -1 & 2  \\\end{matrix} \right)=\frac{1}{5}\left( \begin{matrix}   4 & -3  \\   -1 & 2  \\\end{matrix} \right) \\\end{align}$

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