Question
Evaluate the following determinant:
$$ det \left( \begin{matrix}2&3&-1\\4&-1&5\\-3&2&4\end{matrix} \right) $$Answer
$$ det \left( \begin{matrix}2&3&-1\\4&-1&5\\-3&2&4\end{matrix} \right) = -126 $$
Explanation
To find the 3x3 determinant, we can use the Rule of Sarrus. .
$$ \begin{aligned} det \left( \begin{matrix}2&3&-1\\4&-1&5\\-3&2&4\end{matrix} \right) &= \left[
\begin{array}{ccc|cc} \cssId{i00}{2} & \cssId{i01}{3} & \cssId{i02}{-1} & \cssId{i03}{2} & \cssId{i04}{3} \\
\cssId{i10}{4} & \cssId{i11}{-1} & \cssId{i12}{5} & \cssId{i13}{4} & \cssId{i14}{-1} \\
\cssId{i20}{-3} & \cssId{i21}{2} & \cssId{i22}{4} & \cssId{i23}{-3} & \cssId{i24}{2}
\end{array} \right | = \\\\
&= \cssId{u0}{2 \cdot \left(-1\right) \cdot 4} \cssId{u1}{+3 \cdot 5 \cdot \left(-3\right)} \cssId{u2}{+\left(-1\right) \cdot 4 \cdot 2} \cssId{u3}{-\left(-3\right) \cdot \left(-1\right) \cdot \left(-1\right)} \cssId{u4}{-2 \cdot 5 \cdot 2} \cssId{u5}{-4 \cdot 4 \cdot 3} = \\\\
&= -8 + \left( -45\right) + \left( -8\right) - \left( -3\right) - 20 - 48 = -126
\end{aligned}
$$
This page was created using
Determinant Calculator