Problems from Computing first-order and second-order determinants

Compute the following determinant.

$| \begin{matrix} 1 & - 2 \\ 1 & - 5 \end{matrix} |$

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$| \begin{matrix} 1 & - 2 \\ 1 & - 5 \end{matrix} | = 1 \cdot (- 5) - (- 2) \cdot 1 = - 5 + 2 = - 3$

$- 3$

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Invent a $2 \times 2$ matrix and compute its determinant.

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$A = (\begin{matrix} 1 & 4 \\ - 2 & 3 \end{matrix})$

The determinant of the $2 \times 2$ matrix is the most immediate:

$d e t (A) = | \begin{matrix} 1 & 4 \\ - 2 & 3 \end{matrix} | = 1 \cdot 3 - 4 \cdot (- 2) = 3 + 8 = 11$

$d e t (A) = 11$

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