Determinants
General
Grade 12
Question:
If in the determinant $\begin{vmatrix} x & 3 & 3 \\ 3 & 3 & x \\ 2 & 3 & 3 \end{vmatrix}$, $C_{11} = C_{22}$, where $C_{ij}$ is cofactor of element $a_{ij}$ then $x =$
2
-2
$\frac{5}{2}$
$-\frac{9}{8}$
Step-by-Step Solution
Key Concept: General
$C_{11} = C_{22} \Rightarrow (-1)^{1+1} \begin{vmatrix} 3 & x \\ 3 & 3 \end{vmatrix} = (-1)^{2+2} \begin{vmatrix} x & 3 \\ 2 & 3 \end{vmatrix}$<br>$\Rightarrow 9 - 3x = 3x - 6 \Rightarrow -6x = -15 \Rightarrow x = \frac{5}{2}$
Correct Answer: C