The answer will be option A,B.
Since rank of matrix A is 2, so |A| = 0.This says that there is a non-trivial and non-zero solution. Non-trivial solution means along with a zero solution(0,0,0) there are many points of intersection in the plane.
Number of independent solutions or number of free variables = Total number of variables – rank of A
= 3 – 2 = 1
For eg:
x1 + x2 + x3 = 0
[1 1 1]$\begin{bmatrix} x1\\ x2\\ x3 \end{bmatrix}$ = [0]
Rank = 1 and total variables are 3.
Let x2 =k, x3=t , then x1= – k – t
Total independent variables are 2 (x2,x3) and dependent variable is 1 (x1).