elementary row operations our goal is to begin with an arbitrary matrix and apply operations that respect row equivalence until we have a matrix in reduced row echelon form rref ...
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...Elementary row operations our goal is to begin with an arbitrary matrix and apply that respect equivalence until we have a in reduced echelon form rref the three are swap exchange any two rows scalar multiplication multiply by constant sum add multiple of one another whydothese preserve linear system question swapping just changing order equations considered which certainly should not alter solutions multiplying equation same number on both sides does change solution s likewise if share common adding other preserves thereisaverysimpleprocessforrowreducingamatrix workingcolumn column this called gauss jordan elimination all entries given zero then associated variable undetermined make note ignore such columns so rst entry non pivot multiples each every now repeat steps example x first write as augmented r nowwe re can see it happens be unique notice kept track were taking important for checking work here variables set terms follows...