Write the solution set of the given homogeneous system in parametric vector form

x1+2x2+12x3=0
2x1+x2+12x3=0
-x1+x2 =0

(x1,x2,x3) = (s,s,-0.25s)

Step-by-step explanation:

Given is a systtem of equations

We are to solve them in parametric form.

From equation 3 we get

x1=x2

Substitute in 1 and 2 to get

3x1+12x3 =0 and 3x1 + 12 x3 =0

Thus we find these two equations are dependent.  So we can have infinite solutions in parametric form only. No unique solution is possible

Let x1 = x2 = s

Since 3x1 +12x3 =0

x1 = -4x3

Or x3 = -0.25s

So solution in parametric form is

(x1,x2,x3) = (s,s,-0.25s) for all real values s.

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