# Thread: canonical/row reduced form need urgent help

1. ## canonical/row reduced form need urgent help

i solved

2. $\displaystyle \left( \begin {array}{cccc|c} 3 & 6 & -3 & 0 & 18 \\ 3 & 6 & -3 & 2 & 0 \\ 0 & 1 & -8 & 3 & 7 \\ 3 & 7 & -11 & 3 & 25 \end {array} \right)$

subtract first row from 2nd and 4th rows then swap 2nd and 3rd rows and divide first row by 3

$\displaystyle \left( \begin {array}{cccc|c} 1 & 2 & -1 & 0 & 6 \\ 0 & 1 & -8 & 3 & 7 \\ 0 & 0 & 0 & 2 & -18 \\ 0 & 1 & -8 & 3 & 7 \end {array} \right)$

subtract double 2nd row from first row and subtract 2nd row from 4th row and divide 3rd row by 2

$\displaystyle \left( \begin {array}{cccc|c} 1 & 0 & 15 & -6 & -12 \\ 0 & 1 & -8 & 3 & 7 \\ 0 & 0 & 0 & 1 & -9 \\ 0 & 0 & 0 & 0 & 0 \end {array} \right)$
add 6 times 3rd row to first row and subtract 3 times 3rd row to 2nd row.

$\displaystyle \left( \begin {array}{cccc|c} 1 & 0 & 15 & 0 & -66 \\ 0 & 1 & -8 & 0 & 34 \\ 0 & 0 & 0 & 1 & -9 \\ 0 & 0 & 0 & 0 & 0 \end {array} \right)$

I'm not really sure where your algorithms could be going wrong. I just do these from left to right, getting 0s in all but one row and a one in the non-zero row then moving to the next column.