MCQ
Find the cofactor of element $-3$ in the determinant $\triangle=\begin{bmatrix}1&4&4\\-3&5&9\\2&1&2\end{bmatrix}$ is:
- ✓$-4$
- B$4$
- C$-5$
- D$-3$
✓
Answer
Correct option: A.
$-4$
The minor of element $-3$ is given by
$\text{M}_{21}=\begin{bmatrix}4&4\\1&2\end{bmatrix}=4(2)-4=4\ ($Obtained by eliminating $\text{R}_2$ and $\text{C}_1)$
$\therefore\text{A}_{21}=(-1)^{2+1} \text{M}_{21}=(-1)^3 4=-4.$
$\text{M}_{21}=\begin{bmatrix}4&4\\1&2\end{bmatrix}=4(2)-4=4\ ($Obtained by eliminating $\text{R}_2$ and $\text{C}_1)$
$\therefore\text{A}_{21}=(-1)^{2+1} \text{M}_{21}=(-1)^3 4=-4.$
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