anonymous
  • anonymous
Solve the system using an augmented matrix. Please show all your steps! Thanks! (: -x -3y = -17 2x -6y = -26
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
can you set up the matrix?
anonymous
  • anonymous
Yes: -1 -3 | -17 2 -6 | 26
jim_thompson5910
  • jim_thompson5910
Your next step is to make the upper left corner equal to 1. How do we do this?

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anonymous
  • anonymous
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
  • jim_thompson5910
What do we multiply -1 by to get 1 ?
jim_thompson5910
  • jim_thompson5910
-1 times ??? = 1
anonymous
  • anonymous
-1.
jim_thompson5910
  • jim_thompson5910
so do this across the entire first row....ie multiply EVERY number in row 1 by -1
jim_thompson5910
  • jim_thompson5910
-1 -3 | -17 2 -6 | 26 1 3 | 17 -1*R1 2 -6 | 26
jim_thompson5910
  • jim_thompson5910
The notation -1*R1 means "-1 times Row 1"
anonymous
  • anonymous
Okay so it would be: 1 3 | 17 right?
jim_thompson5910
  • jim_thompson5910
yes it would be
jim_thompson5910
  • jim_thompson5910
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
  • jim_thompson5910
oh sry, i made a typo the second row should be 2 -6 | -26 instead of 2 -6 | 26
anonymous
  • anonymous
You would make the 2 a zero my by multiplying it by 0..? I think..
jim_thompson5910
  • jim_thompson5910
well if you did that, everything in row 2 would become 0
jim_thompson5910
  • jim_thompson5910
then you'd get 0x + 0y = 0...which is completely useless now
anonymous
  • anonymous
Oh. That's true..
jim_thompson5910
  • jim_thompson5910
Instead, you can add/subtract multiples of row 1 to row 2
anonymous
  • anonymous
So does that mean we would subtract 2 from row 2?
jim_thompson5910
  • jim_thompson5910
Notice in the first column we have 1 2
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
Okay. So does that mean that row 2 looks like this now: 0 -6 | -26
jim_thompson5910
  • jim_thompson5910
not quite
jim_thompson5910
  • jim_thompson5910
-6 - 2*(-3) = -12 so the 2nd element in row 2 is -12
anonymous
  • anonymous
Ugh, I'm so confused - lol, these kinds of probles frustrate me! :P
jim_thompson5910
  • jim_thompson5910
-26 - 2*17 = -60
jim_thompson5910
  • jim_thompson5910
so the 3rd element in row 2 is -60
jim_thompson5910
  • jim_thompson5910
after this, you should have 1 3 | 17 0 -12 | -60
jim_thompson5910
  • jim_thompson5910
what's next?

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