Say there are these systems of equations :(adsbygoogle = window.adsbygoogle || []).push({});

x - 2y + z = 0

2y - 8z = 8

-4x + 5y + 9z = -9

In matrix form, it can be represented like this :

--

[1 -2 1 0] < -- row 1

[0 2 -8 8] < -- row 2

[-4 5 9 -9] < -- row 3

When we do elementary row operations, say on row3 = row3 + 4*row1. That changes

row 3 to [0 -3 13 -9], if we substitute this for old row 3 we get a simpler matrix, buts

slightly modified. My question is that, when we do a row operation, how is the

resultant matrix essentially the same, i.e has the same solution set ?

I mean when we do row3 += 4*row1, does that not alter row3 to become a different

row with different solution ? Maybe I missed something in algebra class. Basically, I do

not see why row3 = row3 + 4*row1, has the same solution as just row3 ? I mean

don't we have to do this, row3 + 4*row1 = row4 + 4row1 ? How come, we are only adding

it to one side ?

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# Homework Help: Quick question about matrix operations.

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