Question
Evaluate the following determinant:
$$ det \left( \begin{matrix}1&4\\0&0\end{matrix} \right) $$Answer
$$ det \left( \begin{matrix}1&4\\0&0\end{matrix} \right) = 0 $$
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:
$$ det \left( \begin{matrix} \cssId{i00}{1} & \cssId{i01}{4} \\ \cssId{i10}{0} & \cssId{i11}{0} \end{matrix} \right) =
\cssId{u0}{1 \cdot 0} - \cssId{u1}{0 \cdot 4} = 0 - 0 = 0$$
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