The system of linear equations x+y+z=2,   2x+3y+2z=5,   2x+3y+α2−1z=α+1

According to Cramer’s ruleD=11123223α2−1=αa2−3D1=211532α+13α2−1=α2−α+1 Clearly, when α=4⇒D≠0⇒ Unique Solution  and |a|=3⇒D=0 and   D1≠0The system has no Solution  System is in-consistent