Consider the linear system x+3y+kz=-5 kx+(3+3k)y+(6+k^2)z=-11 x+4y+k^2z=k-4 For which values of k does this system have one solution?
det(A)`!=0 ` if (k-2)(k+1)`!=0 `
so rank of A =3
and rank of augument matrix =3 for all values of k.
if rank (A)=rank(A|b)=3 ,then system has unique solution .
system has unique solution for all values of k except -1,2 .