## octoberchick1011 3 years ago Solve the system using an augmented matrix. Please show all your steps! Thanks! (: -x -3y = -17 2x -6y = -26

1. amistre64

can you set up the matrix?

2. octoberchick1011

Yes: -1 -3 | -17 2 -6 | 26

3. jim_thompson5910

Your next step is to make the upper left corner equal to 1. How do we do this?

4. octoberchick1011

Umm.. I'm not entirely sure - I'm not very good at these types of problems. I think we would multiply by -3 right...?

5. jim_thompson5910

What do we multiply -1 by to get 1 ?

6. jim_thompson5910

-1 times ??? = 1

7. octoberchick1011

-1.

8. jim_thompson5910

so do this across the entire first row....ie multiply EVERY number in row 1 by -1

9. jim_thompson5910

-1 -3 | -17 2 -6 | 26 1 3 | 17 -1*R1 2 -6 | 26

10. jim_thompson5910

The notation -1*R1 means "-1 times Row 1"

11. octoberchick1011

Okay so it would be: 1 3 | 17 right?

12. jim_thompson5910

yes it would be

13. 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 ?

14. jim_thompson5910

oh sry, i made a typo the second row should be 2 -6 | -26 instead of 2 -6 | 26

15. octoberchick1011

You would make the 2 a zero my by multiplying it by 0..? I think..

16. jim_thompson5910

well if you did that, everything in row 2 would become 0

17. jim_thompson5910

then you'd get 0x + 0y = 0...which is completely useless now

18. octoberchick1011

Oh. That's true..

19. jim_thompson5910

20. octoberchick1011

So does that mean we would subtract 2 from row 2?

21. jim_thompson5910

Notice in the first column we have 1 2

22. 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

23. octoberchick1011

Okay. So does that mean that row 2 looks like this now: 0 -6 | -26

24. jim_thompson5910

not quite

25. jim_thompson5910

-6 - 2*(-3) = -12 so the 2nd element in row 2 is -12

26. octoberchick1011

Ugh, I'm so confused - lol, these kinds of probles frustrate me! :P

27. jim_thompson5910

-26 - 2*17 = -60

28. jim_thompson5910

so the 3rd element in row 2 is -60

29. jim_thompson5910

after this, you should have 1 3 | 17 0 -12 | -60

30. jim_thompson5910

what's next?