Find the value of the determinant.
-$$\left| \begin{array} { r r r }
- 2 & 5 & 4 \
3 & - 2 & 1 \
1 & 6 & - 3
\end{array} \right|$$
A) -12
B) -90
C) 130
D) 80

Question

Find the value of the determinant.
-$$\left| \begin{array} { r r r } 
- 2 & 5 & 4 \
3 & - 2 & 1 \
1 & 6 & - 3
\end{array} \right|$$
A) -12
B) -90
C) 130
D) 80

Quizplus · Accepted Answer

The determinant of the matrix can be calculated using the formula for a 3x3 matrix: $$det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$, where the matrix is $$\left| \begin{array} {ccc} a & b & c \ d & e & f \ g & h & i \end{array} \right|$$. Substituting the given values, we get: $$det(A) = (-2)((-2)(-3) - (1)(6)) - (5)((3)(-3) - (1)(1)) + (4)((3)(6) - (-2)(1))$$, which simplifies to $$(-2)(-6 - 6) - (5)(-9 - 1) + (4)(18 + 2)$$, leading to $$(-2)(-12) - (5)(-10) + (4)(20)$$ = $24 + 50 + 80 = 130$.

Find the Value of the Determinant ∣−2543−2116−3∣\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|​−231​5−26​41−3​​

Find the Value of the Determinant $\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|$