Given matrix A, find the indicated cofactor.
-Find $\mathrm { A } _ { 34 }$.
$$A = \left[ \begin{array} { r r r r }
2 & 0 & 4 & - 1 \
9 & 2 & 0 & 1 \
0 & - 7 & 4 & - 2 \
- 3 & 2 & 0 & 0
\end{array} \right]$$
A) 0
B) 192
C) 96
D) $- 96$

Question

Given matrix A, find the indicated cofactor.
-Find $\mathrm { A } _ { 34 }$.
$$A = \left[ \begin{array} { r r r r } 
2 & 0 & 4 & - 1 \
9 & 2 & 0 & 1 \
0 & - 7 & 4 & - 2 \
- 3 & 2 & 0 & 0
\end{array} \right]$$
A) 0
B) 192
C) 96
D) $- 96$

Quizplus · Accepted Answer

The cofactor $A_{34}$ is calculated by removing the third row and fourth column, and then taking the determinant of the remaining 3x3 matrix, followed by multiplying it by $(-1)^{3+4}$. The remaining matrix is:$$\left[ \begin{array}{rrr}2 & 0 & 4 \9 & 2 & 0 \-3 & 2 & 0 \\end{array} \right]$$The determinant of this matrix is $2(2 \cdot 0 - 0 \cdot 2) - 0(9 \cdot 0 - (-3) \cdot 0) + 4(9 \cdot 2 - (-3) \cdot 2) = 0 + 0 + 4(18 + 6) = 4 \cdot 24 = 96$. Multiplying by $(-1)^{3+4} = (-1)^7 = -1$, we get $-96$.

Given Matrix A, Find the Indicated Cofactor A34\mathrm { A } _ { 34 }A34​

Given Matrix A, Find the Indicated Cofactor $\mathrm { A } _ { 34 }$