octoberchick1011
Solve the system using an augmented matrix. Please show all your steps! Thanks! (:
-x -3y = -17
2x -6y = -26
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amistre64
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can you set up the matrix?
octoberchick1011
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Yes:
-1 -3 | -17
2 -6 | 26
jim_thompson5910
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Your next step is to make the upper left corner equal to 1. How do we do this?
octoberchick1011
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Umm.. I'm not entirely sure - I'm not very good at these types of problems.
I think we would multiply by -3 right...?
jim_thompson5910
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What do we multiply -1 by to get 1 ?
jim_thompson5910
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-1 times ??? = 1
jim_thompson5910
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so do this across the entire first row....ie multiply EVERY number in row 1 by -1
jim_thompson5910
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-1 -3 | -17
2 -6 | 26
1 3 | 17 -1*R1
2 -6 | 26
jim_thompson5910
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The notation -1*R1 means "-1 times Row 1"
octoberchick1011
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Okay so it would be:
1 3 | 17 right?
jim_thompson5910
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yes it would be
jim_thompson5910
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The upper left corner is a 1. This is known as the pivot (for the first column). Everything thing else must be a zero in order to obtain the solutions for x and y.
So how to we turn that 2 (below the pivot of 1) into a 0 ?
jim_thompson5910
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oh sry, i made a typo
the second row should be
2 -6 | -26
instead of
2 -6 | 26
octoberchick1011
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You would make the 2 a zero my by multiplying it by 0..? I think..
jim_thompson5910
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well if you did that, everything in row 2 would become 0
jim_thompson5910
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then you'd get 0x + 0y = 0...which is completely useless now
octoberchick1011
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Oh. That's true..
jim_thompson5910
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Instead, you can add/subtract multiples of row 1 to row 2
octoberchick1011
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So does that mean we would subtract 2 from row 2?
jim_thompson5910
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Notice in the first column we have
1
2
jim_thompson5910
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If we subtract row 1 from row 2, we get
2 - 1 = 1
But that's not zero
However, if we subtract row 1 (twice) from row 2, we get
2 - 1 - 1 = 0
octoberchick1011
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Okay.
So does that mean that row 2 looks like this now:
0 -6 | -26
jim_thompson5910
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not quite
jim_thompson5910
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-6 - 2*(-3) = -12
so the 2nd element in row 2 is -12
octoberchick1011
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Ugh, I'm so confused - lol, these kinds of probles frustrate me! :P
jim_thompson5910
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-26 - 2*17 = -60
jim_thompson5910
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so the 3rd element in row 2 is -60
jim_thompson5910
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after this, you should have
1 3 | 17
0 -12 | -60
jim_thompson5910
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what's next?