Math Assignment Help With Homogeneous System Of Linear Equation

3.7.3.2 Homogeneous System Of Linear Equation:

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

So,

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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