Find the determinant of the matrix by the method of expansion by cofactors.Expand using the column 2. $\left[ \begin{array} { c c c }
- 3 & 2 & 1 \
4 & 5 & 6 \
2 & - 3 & 1
\end{array} \right]$
A)-75
B)75
C)-73
D)-74
E)-76

Question

Find the determinant of the matrix by the method of expansion by cofactors.Expand using the column 2.   $\left[ \begin{array} { c c c } 
- 3 & 2 & 1 \
4 & 5 & 6 \
2 & - 3 & 1
\end{array} \right]$  
A)-75
B)75
C)-73
D)-74
E)-76

Quizplus · Accepted Answer

Expanding by cofactors along column 2, we get: $2((-3)(1) - (6)(2)) - 5((-3)(1) - (1)(2)) + (-3)((-3)(6) - (4)(1)) = 2(-3 - 12) - 5(-3 - 2) - 3(-18 - 4) = 2(-15) + 5(5) + 3(22) = -30 + 25 + 66 = -5 + 66 = 61$. However, there seems to be a mistake in my calculation as none of the options match the result. Let's correct the calculation:Expanding by cofactors along column 2 correctly, we get: $2((4)(1) - (6)(2)) - 5((-3)(1) - (1)(2)) + (-3)((-3)(6) - (4)(1)) = 2(4 - 12) - 5(-3 - 2) - 3(-18 - 4) = 2(-8) - 5(-5) - 3(-22) = -16 + 25 + 66 = 9 + 66 = 75$. The correct calculation indeed shows that the determinant is 75, which matches option B, not A as initially stated. My initial response contained a calculation error. The correct choice, based on the corrected calculation, should be B, not A.

Find the Determinant of the Matrix by the Method of Expansion