Question 466168
{{{(matrix(2,3, -6,-3,21,2,1,7))}}}
~ {{{(matrix(2,3, 2,1,7,-6,-3,21))}}}, R1 <-> R2.

~{{{(matrix(2,3, 2,1,7,0,0,42))}}},after 3R1 + R2

~{{{(matrix(2,3, 1,1/2,7/2,0,0,1))}}}, after R1/2 and R2/42

~{{{(matrix(2,3, 1,1/2,0,0,0,1))}}}, after -7R2/2 + R1

The matrix is in reduced row echelon form.  The last row says that the system is inconsistent, and there is no solution set.