current version's usage example (only the first line is user-input):

User input: [[3 1 1 2] [1 -2 1 4] [-1 1 0 4]]
┏             ┓
┃  3  1 1 │ 2 ┃
┃  1 -2 1 │ 4 ┃
┃ -1  1 0 │ 4 ┃
┗             ┛
1/3R₀
┏                  ┓
┃  1 1/3 1/3 │ 2/3 ┃
┃  1  -2   1 │   4 ┃
┃ -1   1   0 │   4 ┃
┗                  ┛
-1R₀ + R₁
┏                    ┓
┃  1  1/3 1/3 │  2/3 ┃
┃  0 -7/3 2/3 │ 10/3 ┃
┃ -1    1   0 │    4 ┃
┗                    ┛
R₀ + R₂
┏                   ┓
┃ 1  1/3 1/3 │  2/3 ┃
┃ 0 -7/3 2/3 │ 10/3 ┃
┃ 0  4/3 1/3 │ 14/3 ┃
┗                   ┛
-3/7R₁
┏                    ┓
┃ 1 1/3  1/3 │   2/3 ┃
┃ 0   1 -2/7 │ -10/7 ┃
┃ 0 4/3  1/3 │  14/3 ┃
┗                    ┛
-4/3R₁ + R₂
┏                    ┓
┃ 1 1/3  1/3 │   2/3 ┃
┃ 0   1 -2/7 │ -10/7 ┃
┃ 0   0  5/7 │  46/7 ┃
┗                    ┛
7/5R₂
┏                    ┓
┃ 1 1/3  1/3 │   2/3 ┃
┃ 0   1 -2/7 │ -10/7 ┃
┃ 0   0    1 │  46/5 ┃
┗                    ┛
-1/3R₂ + R₀
┏                    ┓
┃ 1 1/3    0 │ -12/5 ┃
┃ 0   1 -2/7 │ -10/7 ┃
┃ 0   0    1 │  46/5 ┃
┗                    ┛
2/7R₂ + R₁
┏                 ┓
┃ 1 1/3 0 │ -12/5 ┃
┃ 0   1 0 │   6/5 ┃
┃ 0   0 1 │  46/5 ┃
┗                 ┛
-1/3R₁ + R₀
┏               ┓
┃ 1 0 0 │ -14/5 ┃
┃ 0 1 0 │   6/5 ┃
┃ 0 0 1 │  46/5 ┃
┗               ┛
x = -14/5
y = 6/5
z = 46/5

OLD *actual* usage example:

matrix.core=> (matrix-repl [[1 1 -1 -5] [5 -1 1 -1] [-1 3 -2 1]] :yeah)
┏               ┓
┃  1  1 -1 │ -5 ┃
┃  5 -1  1 │ -1 ┃
┃ -1  3 -2 │  1 ┃
┗               ┛
(add-mul 5 2 1)
┏               ┓
┃  1  1 -1 │ -5 ┃
┃  0 14 -9 │  4 ┃
┃ -1  3 -2 │  1 ┃
┗               ┛
(add 0 2)
┏               ┓
┃  1  1 -1 │ -5 ┃
┃  0 14 -9 │  4 ┃
┃  0  4 -3 │ -4 ┃
┗               ┛
(add-mul -4/14 1 2)
┏                           ┓
┃     1     1    -1 │    -5 ┃
┃     0    14    -9 │     4 ┃
┃     0     0  -3/7 │ -36/7 ┃
┗                           ┛
(mul 7 2)
┏                   ┓
┃   1   1  -1 │  -5 ┃
┃   0  14  -9 │   4 ┃
┃   0   0  -3 │ -36 ┃
┗                   ┛
(mul -1/3 2)
┏               ┓
┃  1  1 -1 │ -5 ┃
┃  0 14 -9 │  4 ┃
┃  0  0  1 │ 12 ┃
┗               ┛
(add-mul 9 2 1)
┏                   ┓
┃   1   1  -1 │  -5 ┃
┃   0  14   0 │ 112 ┃
┃   0   0   1 │  12 ┃
┗                   ┛
(mul 1/14 1)
┏               ┓
┃  1  1 -1 │ -5 ┃
┃  0  1  0 │  8 ┃
┃  0  0  1 │ 12 ┃
┗               ┛
(add 2 0)
┏               ┓
┃  1  1  0 │  7 ┃
┃  0  1  0 │  8 ┃
┃  0  0  1 │ 12 ┃
┗               ┛
(add-mul -1 1 0)
┏               ┓
┃  1  0  0 │ -1 ┃
┃  0  1  0 │  8 ┃
┃  0  0  1 │ 12 ┃
┗               ┛
print-equations
x = -1
y = 8
z = 12
┏               ┓
┃  1  0  0 │ -1 ┃
┃  0  1  0 │  8 ┃
┃  0  0  1 │ 12 ┃
┗               ┛