System of Equations with More Variables

[thingsofleon]

I am missing something. https://www.coursera.org/learn/machine-learning-linear-algebra/lecture/fXzI7/solving-systems-of-equations-with-more-variables

When he reduces down to remove ‘a’ he does row2-row1 and row3-row1(subtracting up) to get row2 and row3 only having b and c. But when he reduces down to remove ‘b’ from row 2 and row 3, he does row2-row3 (subtracting down) instead of row3-row2 (subtracting up like the first reduction).

Does it matter which way you subtract rows? Does it need to be consistent? or do you subtract up always unless you are left with 2 rows where you would then subtract down?

anyone know what my confusion could be?

[shanup]

hello @thingsofleon

While it is always nice to be consistent, in this case it really does not affect the final answer whether you subtract the 1st row from the 2nd OR the 2nd row from the 1st. Since the “-” will impact both sides of the equation (left of the =, and right of the =) , the final answer remains unaffected.

You can try for yourself by swapping the rows in the subtraction and see if the final answer changes…it will not.