A basic [[Algorithm]] for finding the [[Equivalent]] [[Reduced Row Echelon Form]] of an [[Augmented Matrix]] using [[Augmented Matrix|Row Operations]]. - Start at the left column - Move a nonzero term to the top (*if needed*) - Use the top row to cancel all the terms below in the column - Lock the top row and current column, - If the column is all zeroes, skip it - Start at the rightmost column, if there is no leading term in this column, keep moving left >[!example]- >$\augmented{ccccc|c}{ >1&0&2&0& \frac{1}{3} & 0 \\ >0&1&-3&0& \frac{2}{3} & \frac{3}{2} \\ >0 & 0 & 0 & 1 & -\frac{4}{3} & \frac{1}{2} \\ >0 & 0 & 0 & 0 & 0 & 0 >} \huge\sim \cases{ >x + 2z + \frac{1}{3}v = 0 \\ >y - 3z + \frac{2}{3}v = \frac{3}{2} \\ >w - \frac{4}{3}v = \frac{1}{2} >} >$ >$\huge\sim\cases{ >x=-2t - \frac{1}{3}s \\ >y = \frac{3}{2}+ 3t - \frac{2}{3}s \\ >w = \frac{1}{2}+ \frac{4}{3}s \\ >z = t \\ >v = s >}$