Consider the following set of equation;
a11x1+ a12x2+ a13x3 = 0
a21x1+ a22x2+ a23x3 = 0
a31x1+ a32x2+ a33x3 = 0
so the given matrix is in the form of AX = 0
If |A| ≠ 0 then A-1 exists
AX = 0
A-1(AX) = A-1 0
(A-1A)X = 0
IX = 0
i.e. X = 0
Thus in this case x1= 0, x2 = 0 and x3 = 0is the only solution.
This type of solution is called as trivial solution.
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