Transform M into row reduced echelon form (rref)

Gauss-Jordan Elimination

Mark first row (*) as next result row

M = * 00000000000000000000000000000001 00000000000000000000011000000010 00000000000000000001010000000100 00000000000000000100100000001000 00000000000000000101001100010000 00000000000000000110111100100000 00000000000000000011111101000000

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

M = * 00000000000000000000000000000001 00000000000000000000011000000010 00000000000000000001010000000100 00000000000000000100100000001000 00000000000000000101001100010000 00000000000000000110111100100000 00000000000000000011111101000000

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

M = 00000000000000000100100000001000 * 00000000000000000000011000000010 00000000000000000001010000000100 00000000000000000000000000000001 00000000000000000101001100010000 00000000000000000110111100100000 00000000000000000011111101000000

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

M = 00000000000000000100100000001000 * 00000000000000000000011000000010 00000000000000000001010000000100 00000000000000000000000000000001 00000000000000000001101100011000 00000000000000000010011100101000 00000000000000000011111101000000

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

M = 00000000000000000100100000001000 * 00000000000000000000011000000010 00000000000000000001010000000100 00000000000000000000000000000001 00000000000000000001101100011000 00000000000000000010011100101000 00000000000000000011111101000000

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

M = 00000000000000000100100000001000 00000000000000000010011100101000 * 00000000000000000001010000000100 00000000000000000000000000000001 00000000000000000001101100011000 00000000000000000000011000000010 00000000000000000011111101000000

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

M = 00000000000000000100100000001000 00000000000000000010011100101000 * 00000000000000000001010000000100 00000000000000000000000000000001 00000000000000000001101100011000 00000000000000000000011000000010 00000000000000000001100001101000

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

M = 00000000000000000100100000001000 00000000000000000010011100101000 * 00000000000000000001010000000100 00000000000000000000000000000001 00000000000000000001101100011000 00000000000000000000011000000010 00000000000000000001100001101000

Increment next result row.

M = 00000000000000000100100000001000 00000000000000000010011100101000 00000000000000000001010000000100 * 00000000000000000000000000000001 00000000000000000001101100011000 00000000000000000000011000000010 00000000000000000001100001101000

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

M = 00000000000000000100100000001000 00000000000000000010011100101000 00000000000000000001010000000100 * 00000000000000000000000000000001 00000000000000000000111100011100 00000000000000000000011000000010 00000000000000000000110001101100

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

M = 00000000000000000100100000001000 00000000000000000010011100101000 00000000000000000001010000000100 * 00000000000000000000000000000001 00000000000000000000111100011100 00000000000000000000011000000010 00000000000000000000110001101100

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

M = 00000000000000000100100000001000 00000000000000000010011100101000 00000000000000000001010000000100 00000000000000000000111100011100 * 00000000000000000000000000000001 00000000000000000000011000000010 00000000000000000000110001101100

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

M = 00000000000000000100011100010100 00000000000000000010011100101000 00000000000000000001010000000100 00000000000000000000111100011100 * 00000000000000000000000000000001 00000000000000000000011000000010 00000000000000000000001101110000

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

M = 00000000000000000100011100010100 00000000000000000010011100101000 00000000000000000001010000000100 00000000000000000000111100011100 * 00000000000000000000000000000001 00000000000000000000011000000010 00000000000000000000001101110000

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

M = 00000000000000000100011100010100 00000000000000000010011100101000 00000000000000000001010000000100 00000000000000000000111100011100 00000000000000000000011000000010 * 00000000000000000000000000000001 00000000000000000000001101110000

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

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001001000000110 00000000000000000000100100011110 00000000000000000000011000000010 * 00000000000000000000000000000001 00000000000000000000001101110000

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

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001001000000110 00000000000000000000100100011110 00000000000000000000011000000010 * 00000000000000000000000000000001 00000000000000000000001101110000

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

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001001000000110 00000000000000000000100100011110 00000000000000000000011000000010 00000000000000000000001101110000 * 00000000000000000000000000000001

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

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001000101110110 00000000000000000000100100011110 00000000000000000000010101110010 00000000000000000000001101110000 * 00000000000000000000000000000001

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

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001000101110110 00000000000000000000100100011110 00000000000000000000010101110010 00000000000000000000001101110000 * 00000000000000000000000000000001

Increment next result row.

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001000101110110 00000000000000000000100100011110 00000000000000000000010101110010 00000000000000000000001101110000 00000000000000000000000000000001

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

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001000101110110 00000000000000000000100100011110 00000000000000000000010101110010 00000000000000000000001101110000 00000000000000000000000000000001

Done.

M = 00000000000000000100000100010110 00000000000000000010000100101010 00000000000000000001000101110110 00000000000000000000100100011110 00000000000000000000010101110010 00000000000000000000001101110000 00000000000000000000000000000001

See also: