Determinants
General
Grade 12
Question:
If $\begin{vmatrix} x+3 & 1 & -2 \\ 3 & -2 & 1 \\ -x & -3 & 3 \end{vmatrix} = 0$, find $x$.
Step-by-Step Solution
Key Concept: General
$\begin{vmatrix} x+3 & 1 & -2 \\ 3 & -2 & 1 \\ -x & -3 & 3 \end{vmatrix} = 0 \Rightarrow (x+3)[-6 - (-3)] - 1[9 + x] - 2[-9 - 2x] = 0 \Rightarrow (x+3)(-6 + 3) - (9 + x) - 2(-9 - 2x) = 0 \Rightarrow -3(x+3) - 9 - x + 18 + 4x = 0 \Rightarrow -3x - 9 - 9 - x + 18 + 4x = 0 \Rightarrow -4x + 4x - 18 + 18 = 0 \therefore x \in R$.
Correct Answer: $x \in R$