Question:
Consider the system of equations:
a1x + b1y + c1z = 0
a2x + b2y + c2z = 0
a3x + b3y + c3z = 0,
if $\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|=0$, then the system has
(a) more than two solutions
(b) one trivial and one non-trivial solutions
(c) no solution
(d) only trivial solution (0, 0, 0)
Solution:
(a) more than two solutions
Here,
$|A|=0$ and $B=0$ (Given)
If $|A|=0$ and (adj $A) B=0$, then the system is consistent and has infinitely many solutions.
Clearly, it has more than two solutions.