Find the value of the determinant.
-$$\left| \begin{array} { l l l }
2 & 2 & 2 \
3 & 4 & 7 \
5 & 8 & 5
\end{array} \right|$$
A) 24
B) 340
C) $- 164$
D) $- 24$

Question

Find the value of the determinant.
-$$\left| \begin{array} { l l l } 
2 & 2 & 2 \
3 & 4 & 7 \
5 & 8 & 5
\end{array} \right|$$
A) 24
B) 340
C) $- 164$
D) $- 24$

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 $2(4*5 - 7*8) - 2(3*5 - 7*5) + 2(3*8 - 4*5) = 2(-36) - 2(-10) + 2(4) = -72 + 20 + 8 = -44$. It appears there was a mistake in my calculation. Let's correct the calculation: $2(4*5 - 7*8) - 2(3*5 - 5*5) + 2(3*8 - 4*5) = 2(20 - 56) - 2(15 - 25) + 2(24 - 20) = 2(-36) + 2(10) + 2(4) = -72 + 20 + 8 = -44$. Correcting the calculation again: The correct calculation should be $2(4*5 - 7*8) - 2(3*5 - 7*5) + 2(3*8 - 4*5)$, which simplifies to $2(20 - 56) - 2(15 - 35) + 2(24 - 20) = 2(-36) + 2(-20) + 2(4) = -72 - 40 + 8 = -104$. It seems there was another mistake in my recalculation. Let's correctly calculate the determinant without errors: The determinant is $2(4*5 - 7*8) - 2(3*5 - 7*5) + 2(3*8 - 4*5) = 2(20 - 56) - 2(15 - 35) + 2(24 - 20) = 2(-36) + 2(20) + 2(4) = -72 + 40 + 8 = -24$.

Find the Value of the Determinant ∣222347585∣\left| \begin{array} { l l l } 2 & 2 & 2 \\3 & 4 & 7 \\5 & 8 & 5\end{array} \right|​235​248​275​​

Find the Value of the Determinant $\left| \begin{array} { l l l } 2 & 2 & 2 \\3 & 4 & 7 \\5 & 8 & 5\end{array} \right|$