Find $| A B |$, if
$$A = \left[ \begin{array} { r r r }
5 & - 2 & - 2 \
- 3 & 4 & - 1 \
- 5 & 6 & 2
\end{array} \right] , B = \left[ \begin{array} { r r r }
1 & - 1 & - 3 \
- 5 & - 3 & 4 \
- 5 & - 1 & - 2
\end{array} \right]$$
A) 3080
B) 616
C) 150
D) 280
E) 1300

Question

Find $| A B |$, if
$$A = \left[ \begin{array} { r r r } 
5 & - 2 & - 2 \
- 3 & 4 & - 1 \
- 5 & 6 & 2
\end{array} \right] , B = \left[ \begin{array} { r r r } 
1 & - 1 & - 3 \
- 5 & - 3 & 4 \
- 5 & - 1 & - 2
\end{array} \right]$$
A) 3080
B) 616
C) 150
D) 280
E) 1300

Quizplus · Accepted Answer

To find $|AB|$, we first need to multiply matrices $A$ and $B$, and then find the determinant of the resulting matrix. The multiplication of $A$ and $B$ is performed by taking the dot product of rows of $A$ with columns of $B$. After performing the multiplication, we get a new matrix $AB$. The determinant of a 3x3 matrix $M = \left[ \begin{array}{ccc} a & b & c \ d & e & f \ g & h & i \end{array} \right]$ is calculated as $|M| = a(ei - fh) - b(di - fg) + c(dh - eg)$.Applying this formula to the resulting matrix $AB$ will give us the determinant $|AB|$. Without the explicit multiplication and determinant calculation steps shown here (since they involve a series of arithmetic operations), the correct answer is found to be 3080 after performing these calculations.

Find ∣AB∣| A B |∣AB∣ , If A) 3080 B) 616 C) 150 D) 280 E) 1300

Find $| A B |$ , If A) 3080
B) 616
C) 150
D) 280
E) 1300