The system of equations $x_1 - x_2 + x_3 = 2, 3x_1 - x_2 + 2x_3 = -6$ and $3x_1 + x_2 + x_3 = -18$ has
Step-by-Step Solution
Key Concept: General
$D = \begin{vmatrix} 1 & -1 & 1 \\ 3 & -1 & 2 \\ 3 & 1 & 1 \end{vmatrix} = 1[-1-2]-1[6-3]+1[3+3]=0$<br>And $D_1 = \begin{vmatrix} 2 & -1 & 1 \\ -6 & -1 & 2 \\ -18 & 1 & 1 \end{vmatrix} = 2(-1-2)-1(-36+6)+1(-6-18) = -6 + 30 - 24 = 0$<br>Also, $D_2 = 0; D_3 = 0$<br>So, the system is consistent ($D = D_1 = D_2 = D_3 = 0$) i.e. system has infinite solution.
Correct Answer: Infinite solutions