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Question
Evaluate the following determinant:
$$ det \left( \begin{matrix}4&8&5\\-3&2&6\\11&-3&5\end{matrix} \right) $$
Answer
$$ det \left( \begin{matrix}4&8&5\\-3&2&6\\11&-3&5\end{matrix} \right) = 695 $$
Explanation
To find the 3x3 determinant, we can use the Rule of Sarrus. .
$$ \begin{aligned} det \left( \begin{matrix}4&8&5\\-3&2&6\\11&-3&5\end{matrix} \right) &= \left[
\begin{array}{ccc|cc} \cssId{i00}{4} & \cssId{i01}{8} & \cssId{i02}{5} & \cssId{i03}{4} & \cssId{i04}{8} \\
\cssId{i10}{-3} & \cssId{i11}{2} & \cssId{i12}{6} & \cssId{i13}{-3} & \cssId{i14}{2} \\
\cssId{i20}{11} & \cssId{i21}{-3} & \cssId{i22}{5} & \cssId{i23}{11} & \cssId{i24}{-3}
\end{array} \right | = \\\\
&= \cssId{u0}{4 \cdot 2 \cdot 5} \cssId{u1}{+8 \cdot 6 \cdot 11} \cssId{u2}{+5 \cdot \left(-3\right) \cdot \left(-3\right)} \cssId{u3}{-11 \cdot 2 \cdot 5} \cssId{u4}{-\left(-3\right) \cdot 6 \cdot 4} \cssId{u5}{-5 \cdot \left(-3\right) \cdot 8} = \\\\
&= 40 + 528 + 45 - 110 - \left( -72\right) - \left( -120\right) = 695
\end{aligned}
$$
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