Question 438728
{{{A = (matrix(3,3, 1,2,k,-1,2k,1,k,-2,1))}}}
~{{{(matrix(3,3, 1,2,k,0,2k+2,k+1,k,-2,1))}}},  R1 + R2
~{{{(matrix(3,3, 1,2,k,k,-2,1,0,2k+2,k+1))}}},  R2 <--> R3

~{{{(matrix(3,3, 1,2,k,0,-2(k+1),(1-k)(1+k),0,2(k+1),k+1))}}}, -kR1 + R2

~{{{(matrix(3,3, 1,2,k,0,-2(k+1),(1-k)(1+k),0,0,(k+1)(2-k)))}}}, R2 + R3

For Rank 3: {{{k<>2}}}, -1
For rank 2: k = 2
For rank 1: k = -1.