Evaluate the determinant.
-$$\left| \begin{array} { l l l }
1 & 5 & 5 \
3 & 6 & 2 \
5 & 6 & 5
\end{array} \right|$$
A)407
B)-167
C)67
D)-67

Question

Evaluate the determinant.
-$$\left| \begin{array} { l l l } 
1 & 5 & 5 \
3 & 6 & 2 \
5 & 6 & 5
\end{array} \right|$$
A)407
B)-167
C)67
D)-67

Quizplus · Accepted Answer

The determinant of a 3x3 matrix $\left| \begin{array} { l l l } a & b & c \ d & e & f \ g & h & i \end{array} \right|$ is calculated as $a(ei - fh) - b(di - fg) + c(dh - eg)$. Applying this formula to the given matrix, we get $1(6*5 - 2*6) - 5(3*5 - 2*5) + 5(3*6 - 6*5)$ = $1(30 - 12) - 5(15 - 10) + 5(18 - 30)$ = $1*18 - 5*5 + 5*(-12)$ = $18 - 25 - 60$ = $-67$.

Evaluate the Determinant ∣155362565∣\left| \begin{array} { l l l } 1 & 5 & 5 \\3 & 6 & 2 \\5 & 6 & 5\end{array} \right|​135​566​525​​

Evaluate the Determinant $\left| \begin{array} { l l l } 1 & 5 & 5 \\3 & 6 & 2 \\5 & 6 & 5\end{array} \right|$