Question 1031370
Matrix B can be shown to be row-equivalent to {{{(matrix(3,4,1,0,-7,0,0,1,-3,1,0,0,0,1))}}}.  A few more column operations would lead to equivalence to {{{(matrix(3,4,1,0,0,0,0,1,0,0,0,0,1,0))}}}.

By performing a sequence of row operations and then a sequence of column operations, matrix {{{C = (matrix( 3,4,
1, 2, 1, 2,
1, 1, 4, 0,
1, -1, -4, 1))}}} can also be shown to be equivalent to {{{(matrix(3,4,1,0,0,0,0,1,0,0,0,0,1,0))}}}.

Therefore matrices B and C are equivalent to the same row- and column-reduced matrix, and so they themselves are equivalent to each other.