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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)
Solution
(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.
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