Question

Consider the system of equations:
a₁x + b₁y + c₁z = 0
a₂x + b₂y + c₂z = 0
a₃x + b₃y + c₃z = 0,
if \[\begin{vmatrix}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{vmatrix}\]= 0, then the system has

Options

• more than two solutions

• one trivial and one non-trivial solutions

• no solution

• only trivial solution (0, 0, 0)

Answer 1

(a) more than two solutions
Here, 
\[\left| A \right| = 0\text{ and }B = 0 \left(\text{ Given }\right)\]
\[\text{ If }\left| A \right|=0\text{ and }\left( adjA \right)B=0,\text{ then the system is consistent and has infinitely many solutions.}\]
Clearly, it has more than two solutions.