Question 1050347
{{{(matrix(3,4,3,a,6,6,-1,3, -1,1,2,-2,6,11))}}}
~{{{(matrix(3,4,0,a+9,3,9,-1,3, -1,1,0,1,1,13/4))}}}, after {{{3R[2]+R[1]}}} and {{{2R[2]+R[3]}}},
~{{{(matrix(3,4,1,-3, 1,-1,0,1,1,13/4,0,a+9,3,9))}}}
~{{{(matrix(3,4,1,0,4, 35/4,0,1,1,13/4,0,0,-a-6,-13a/4-81/4))}}}, after {{{-(a+9)R[2]+R[3]}}}.  
(We may assume that {{{a+9<>0}}}.  If a+9=0, or a = -9, then the system will have a unique solution.)


Case 1. -a-6 = 0. ===> a = -6.

===> {{{-13a/4 - 81/4 = -3/4  <> 0}}}

===> System has no solution.


Case 2. {{{-a-6 <> 0}}} ===> {{{a<>-6}}} ===> {{{(matrix(3,4,1,0,4, 35/4,0,1,1,13/4,0,0,1,(13a/4+81/4)/(a+6)))}}}  ===> System has unique solution.


There is no instance that the system will have infinite number of solutions.