Question
Evaluate the following determinant:
$$ det \left( \begin{matrix}-5&-3\\5&2\end{matrix} \right) $$Answer
$$ det \left( \begin{matrix}-5&-3\\5&2\end{matrix} \right) = 5 $$
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:
$$ det \left( \begin{matrix} \cssId{i00}{-5} & \cssId{i01}{-3} \\ \cssId{i10}{5} & \cssId{i11}{2} \end{matrix} \right) =
\cssId{u0}{-5 \cdot 2} - \cssId{u1}{5 \cdot \left( -3\right)} = -10 - \left( -15\right) = 5$$
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