Calculate $| \mathbf { A } |$
-$$\mathrm { A } = \left| \begin{array} { l l l }
2 & 2 & 2 \
6 & 6 & 1 \
3 & 2 & 1
\end{array} \right|$$
A)10
B)-10
C)-22
D)94

Question

Calculate $| \mathbf { A } |$
-$$\mathrm { A } = \left| \begin{array} { l l l } 
2 & 2 & 2 \
6 & 6 & 1 \
3 & 2 & 1
\end{array} \right|$$
A)10
B)-10
C)-22
D)94

Quizplus · Accepted Answer

To find the determinant of a 3x3 matrix, use the rule of Sarrus or cofactor expansion. Here, using cofactor expansion along the first row: $ |A| = 2(6*1 - 2*1) - 2(6*1 - 3*1) + 2(6*2 - 3*6) = 2(6 - 2) - 2(6 - 3) + 2(12 - 18) = 2*4 - 2*3 + 2*(-6) = 8 - 6 - 12 = -10 $.

Calculate ∣A∣| \mathbf { A } |∣A∣ - A=∣222661321∣\mathrm { A } = \left| \begin{array} { l l l } 2 & 2 & 2 \\6 & 6 & 1 \\3 & 2 & 1\end{array} \right|A=​263​262​211​​

Calculate $| \mathbf { A } |$ - $\mathrm { A } = \left| \begin{array} { l l l } 2 & 2 & 2 \\6 & 6 & 1 \\3 & 2 & 1\end{array} \right|$