If a, b, c are in G.P. with common ratio r1 and α, β, γ are in G.P. with common ratio r2, and equations ax + αy + z = 0, bx + βy + z = 0, cx + γy + z = 0 have only zero solution, then which of the following is not true?

As a, b, c are in G.P. with common ratio r1 and α, β, γ are in G.P. having common ratio r2,a≠0,α≠0,b=ar1,c=ar12,β=ar2,γ=ar22.Also the system of equations has only zero (trivial) solution.Δ=aα1bβ1cγ1≠0⇒ aα111r1r21r12r221≠0⇒ aαr1−1r2−1r1−r2≠0⇒ r1≠1,r2≠1, and r1≠r2