Question
Evaluate the following determinant:
$$ det \left( \begin{matrix}-\dfrac{ 3 }{ 2 }&2\\-5&4\end{matrix} \right) $$Answer
$$ det \left( \begin{matrix}-\dfrac{ 3 }{ 2 }&2\\-5&4\end{matrix} \right) = 4 $$
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:
$$ det \left( \begin{matrix} \cssId{i00}{-\frac{ 3 }{ 2 }} & \cssId{i01}{2} \\ \cssId{i10}{-5} & \cssId{i11}{4} \end{matrix} \right) =
\cssId{u0}{-\frac{ 3 }{ 2 } \cdot 4} - \cssId{u1}{\left( -5\right) \cdot 2} = -6 - \left( -10\right) = 4$$
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