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


Question

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

Options

A) \(\frac{1}{5}\) \(\begin{vmatrix} 2 & 1 \\ 3 & 4\end{vmatrix}\)

B) \(\frac{1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2\end{vmatrix}\)

C) \(\frac{1}{5}\) \(\begin{vmatrix} 2 & -1 \\ -3 & 4\end{vmatrix}\)

D) \(\frac{1}{5}\) \(\begin{vmatrix} 4 & 3 \\ 1 & 2\end{vmatrix}\)

The correct answer is B.

Explanation:

N = [2 3]
N-1 = \(\frac{adj N}{|N|}\)
adj N = \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)
|N| = (2 x4) - (1 x 3)
= 8 - 3
=5
N-1 = \(\frac {1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

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Dicussion (1)

  • N = [2 3]
    N-1 = \(\frac{adj N}{|N|}\)
    adj N = \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)
    |N| = (2 x4) - (1 x 3)
    = 8 - 3
    =5
    N-1 = \(\frac {1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

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