[tex] \left \{ {{x+ay+2z=1} \atop {x+(2a-1)y+3z=1}}\atop {x+ay+(a-3)z=1}} \right. [/tex]
det(A)=0 <=>[tex] \left[\begin{array}{ccc}1&a&2\\1&2a-1&3\\1&a&a-3\end{array}\right] [/tex]=(2a-1)(a-3)+2a+3a-2(2a-1)-3a-a(a-3)=2[tex] a^{2} [/tex]-6a-a+3+2a+3a-4a+2-3a-[tex] a^{2} [/tex]+3a=[tex] a^{2} [/tex]-6a+5=0
Δ=36-20=16
a1=5 si a2=1
