Transform M into row reduced echelon form (rref)

Gauss-Jordan Elimination

Mark first row (*) as next result row

M = * 00000000000000000000000000000001 00000000000000000000001100000010 00000000000000000000101000000100 00000000000000000001011110001000 00000000000000000001001010010000 00000000000000000001110100100000

Highlight next pivot row and column
Find first row with leftmost bit set starting from next result row.

M = * 00000000000000000000000000000001 00000000000000000000001100000010 00000000000000000000101000000100 00000000000000000001011110001000 00000000000000000001001010010000 00000000000000000001110100100000

Swap pivot row and next result row; Increment next result row.

M = 00000000000000000001011110001000 * 00000000000000000000001100000010 00000000000000000000101000000100 00000000000000000000000000000001 00000000000000000001001010010000 00000000000000000001110100100000

Clear pivot column.
Add pivot row to all other rows with bit set in pivot column

M = 00000000000000000001011110001000 * 00000000000000000000001100000010 00000000000000000000101000000100 00000000000000000000000000000001 00000000000000000000010100011000 00000000000000000000101010101000

Highlight next pivot row and column
Find first row with leftmost bit set starting from next result row.

M = 00000000000000000001011110001000 * 00000000000000000000001100000010 00000000000000000000101000000100 00000000000000000000000000000001 00000000000000000000010100011000 00000000000000000000101010101000

Swap pivot row and next result row; Increment next result row.

M = 00000000000000000001011110001000 00000000000000000000101000000100 * 00000000000000000000001100000010 00000000000000000000000000000001 00000000000000000000010100011000 00000000000000000000101010101000

Clear pivot column.
Add pivot row to all other rows with bit set in pivot column

M = 00000000000000000001011110001000 00000000000000000000101000000100 * 00000000000000000000001100000010 00000000000000000000000000000001 00000000000000000000010100011000 00000000000000000000000010101100

Highlight next pivot row and column
Find first row with leftmost bit set starting from next result row.

M = 00000000000000000001011110001000 00000000000000000000101000000100 * 00000000000000000000001100000010 00000000000000000000000000000001 00000000000000000000010100011000 00000000000000000000000010101100

Swap pivot row and next result row; Increment next result row.

M = 00000000000000000001011110001000 00000000000000000000101000000100 00000000000000000000010100011000 * 00000000000000000000000000000001 00000000000000000000001100000010 00000000000000000000000010101100

Clear pivot column.
Add pivot row to all other rows with bit set in pivot column

M = 00000000000000000001001010010000 00000000000000000000101000000100 00000000000000000000010100011000 * 00000000000000000000000000000001 00000000000000000000001100000010 00000000000000000000000010101100

Highlight next pivot row and column
Find first row with leftmost bit set starting from next result row.

M = 00000000000000000001001010010000 00000000000000000000101000000100 00000000000000000000010100011000 * 00000000000000000000000000000001 00000000000000000000001100000010 00000000000000000000000010101100

Swap pivot row and next result row; Increment next result row.

M = 00000000000000000001001010010000 00000000000000000000101000000100 00000000000000000000010100011000 00000000000000000000001100000010 * 00000000000000000000000000000001 00000000000000000000000010101100

Clear pivot column.
Add pivot row to all other rows with bit set in pivot column

M = 00000000000000000001000110010010 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 * 00000000000000000000000000000001 00000000000000000000000010101100

Highlight next pivot row and column
Find first row with leftmost bit set starting from next result row.

M = 00000000000000000001000110010010 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 * 00000000000000000000000000000001 00000000000000000000000010101100

Swap pivot row and next result row; Increment next result row.

M = 00000000000000000001000110010010 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 00000000000000000000000010101100 * 00000000000000000000000000000001

Clear pivot column.
Add pivot row to all other rows with bit set in pivot column

M = 00000000000000000001000100111110 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 00000000000000000000000010101100 * 00000000000000000000000000000001

Highlight next pivot row and column
Find first row with leftmost bit set starting from next result row.

M = 00000000000000000001000100111110 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 00000000000000000000000010101100 * 00000000000000000000000000000001

Increment next result row.

M = 00000000000000000001000100111110 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 00000000000000000000000010101100 00000000000000000000000000000001

Clear pivot column.
Add pivot row to all other rows with bit set in pivot column

M = 00000000000000000001000100111110 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 00000000000000000000000010101100 00000000000000000000000000000001

Done.

M = 00000000000000000001000100111110 00000000000000000000100100000110 00000000000000000000010100011000 00000000000000000000001100000010 00000000000000000000000010101100 00000000000000000000000000000001

See also: