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Let us consider the system of equation
2x+3y = 0
In this system of equation , x=y=0 is trivial solution.
But this solution is not unique as well.
Since one equation is multiple of the other so ,
has infinite no. of solution.
Thus we can conclude that trivial solution is always not unique.
Homogeneous system - may be unique.
Non Homogeneous system not unique.
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