Printing the initial problem matrix and the intermediates after swapping:
[[34, 28, 42, 18, 23, 17, 27], [15, 38, 24, 11, 12, 22, 16], [44, 21, 25, 13, 19, 10, 14], [43, 30, 29, 39, 20, 26, 32], [37, 40, 41, 35, 33, 36, 31]]


Swap: 
[42, 15]


[[34, 28, 15, 18, 23, 17, 27], [42, 38, 24, 11, 12, 22, 16], [44, 21, 25, 13, 19, 10, 14], [43, 30, 29, 39, 20, 26, 32], [37, 40, 41, 35, 33, 36, 31]]


Swap: 
[25, 14]


[[34, 28, 15, 18, 23, 17, 27], [42, 38, 24, 11, 12, 22, 16], [44, 21, 14, 13, 19, 10, 25], [43, 30, 29, 39, 20, 26, 32], [37, 40, 41, 35, 33, 36, 31]]


Swap: 
[39, 33]


[[34, 28, 15, 18, 23, 17, 27], [42, 38, 24, 11, 12, 22, 16], [44, 21, 14, 13, 19, 10, 25], [43, 30, 29, 33, 20, 26, 32], [37, 40, 41, 35, 39, 36, 31]]


Swap: 
[23, 16]


[[34, 28, 15, 18, 16, 17, 27], [42, 38, 24, 11, 12, 22, 23], [44, 21, 14, 13, 19, 10, 25], [43, 30, 29, 33, 20, 26, 32], [37, 40, 41, 35, 39, 36, 31]]


Swap: 
[40, 34]


[[40, 28, 15, 18, 16, 17, 27], [42, 38, 24, 11, 12, 22, 23], [44, 21, 14, 13, 19, 10, 25], [43, 30, 29, 33, 20, 26, 32], [37, 34, 41, 35, 39, 36, 31]]


Swap: 
[24, 10]


[[40, 28, 15, 18, 16, 17, 27], [42, 38, 10, 11, 12, 22, 23], [44, 21, 14, 13, 19, 24, 25], [43, 30, 29, 33, 20, 26, 32], [37, 34, 41, 35, 39, 36, 31]]


Swap: 
[32, 29]


[[40, 28, 15, 18, 16, 17, 27], [42, 38, 10, 11, 12, 22, 23], [44, 21, 14, 13, 19, 24, 25], [43, 30, 32, 33, 20, 26, 29], [37, 34, 41, 35, 39, 36, 31]]