## Dido525 2 years ago Linear algebra question?

1. Dido525

2. Dido525

Anyone want to help me get started? I am pretty sure I can do the rest on my own.

3. Cecily

Represent the system in matrix form

4. Dido525

Yep, that's what I did.

5. Dido525

@Cecily

6. Dido525

How do I go on from there?

7. Dido525

@zepdrix @Outkast3r09

8. Dido525

@dumbcow

9. sirm3d

take the determinant of the coefficient matrix, and set it equal to zero.

10. Dido525

Woah woah!!! We haven't learned what a determinant is yet. :P .

11. sirm3d

12. Dido525

Yeah. We learned that.

13. sirm3d

i got something easier than gauss-jordan. multiply equation 2 by (-1), and equation 3 by 2, then add the two equations.

14. Dido525

Elimination?

15. sirm3d

yup.

16. Dido525

3y-3z=-a+2 ?

17. sirm3d

not 3y+3z = -a + 2 ?

18. Dido525

Yeah. My mistake.

19. Dido525

Allright, what next?

20. sirm3d

use that equation with equation 1 to eliminate both y and z.

21. Dido525

1 sec.

22. Dido525

THat dosen't eliminate it. It makes it bigger.

23. sirm3d

bx + 3y + 3z = a 3y + 3z = 2 - a subtract.

24. Dido525

I used substitution instead. Should till be valid right?

25. sirm3d

or if you wish to substitute...

26. sirm3d

that's valid too.

27. sirm3d

bx + (2-a) =a bx = 2a - 2

28. Dido525

|dw:1358650895030:dw|

29. sirm3d

you're not to eliminate a, but y and z.

30. Dido525

Right.

31. Dido525

Lets us elimination then lol.

32. Dido525

bx=2a-2?

33. sirm3d

yup.

34. Dido525

Now would I solve for a and substitute this into equation 2?

35. sirm3d

now if you put b = 1, and a any real number other than 1, say 3, 0x = 4 0 = 4 which is clearly false.

36. sirm3d

err. i mean put b = 0.

37. Dido525

Why can I put 1?

38. Dido525

for a*

39. Dido525

Ohh never mind. I see why.

40. Dido525

For infinitely many solutions I would make 0=0 right?

41. sirm3d

42. Dido525

Okay what about a unique solution? @sirm3d

43. sirm3d

unique solution when b is not equal to zero.

44. Dido525

and a is 1 right?

45. sirm3d

any value of a for as long as b not zero will yield a unique solution

46. Dido525

Thanks so much!

47. sirm3d

yw.