Question
Evaluate the following determinant:
$$ det \left( \begin{matrix}\dfrac{ 627 }{ 10 }&8\\\dfrac{ 644 }{ 423 }&24\end{matrix} \right) $$Answer
$$ det \left( \begin{matrix}\dfrac{ 627 }{ 10 }&8\\\dfrac{ 644 }{ 423 }&24\end{matrix} \right) = \frac{ 3156892 }{ 2115 } $$
Explanation
The determinant of 2x2 matrix is calculated as:
$$ \color{blue}{ det \left( \begin{matrix} a & b \\ c & d \end{matrix} \right) = a \cdot d - c \cdot b } $$In our case we have:
$$ det \left( \begin{matrix} \cssId{i00}{\frac{ 627 }{ 10 }} & \cssId{i01}{8} \\ \cssId{i10}{\frac{ 644 }{ 423 }} & \cssId{i11}{24} \end{matrix} \right) =
\cssId{u0}{\frac{ 627 }{ 10 } \cdot 24} - \cssId{u1}{\frac{ 644 }{ 423 } \cdot 8} = \frac{ 7524 }{ 5 } - \frac{ 5152 }{ 423 } = \frac{ 3156892 }{ 2115 }$$
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