## Dido525 2 years ago Solve the following system by Gauss–Jordan elimination. 2x₁+5x₂+3x₃=35 12x₁+31x₂+20x₃=216

1. Dido525

I got x₁=5/2 x₂=6 x₃=t (free variable) The answer says I am wrong. Care to tell me what I did wrong?

2. Dido525

@jim_thompson5910

3. Dido525

@ParthKohli @UnkleRhaukus

4. UnkleRhaukus

x_3=0

5. Dido525

Right. But whats wrong with my other answers?

6. Dido525

Here is what the online page looks like:

7. wio

Shouldn't the other variables be in terms of the free variable?

8. wio

What did were your elimination steps?

9. Dido525

It's difficult to post the elimination steps here. I checked with my calculator though. It's correct.

10. Dido525

But yeah, that's what I think @wio . I don't know how to express it though.

11. UnkleRhaukus

when we check your solution , we see t must be 0 x₁=5/2 x₂=6 x₃=t _________ 2x₁+5x₂+3x₃=35 5+30+3t = 35 35 +3t = 35 _________ 12x₁+31x₂+20x₃ = 216 60 + 186 + 20t = 216 216 + 20t = 216

12. Dido525

but t is a free variable is it not? SO it can be any value it wants.

13. wio

$\begin{bmatrix} 2&5&3 \\ 12&31&20 \\ 0&0&1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 35 \\ 216 \\ t \end{bmatrix}$

14. wio

Did you solve it like this?

15. Dido525

No... How did you get 0,0 and 1?

16. wio

I just added in the equation $$x_3=t$$

17. Dido525

Sorry, that doesn't make sense.

18. wio

I added in the equation: $0x_1+ 0x_2 +1x_3 = t$

19. Dido525

Ohh I see.

20. wio

All of the elimination you did before should work for the most part.

21. Dido525

So I do a back substitution?

22. wio

You first want to get the second row to have a zero in it's first colum

23. Dido525

because x3=t so solve the others n terms of t.

24. wio

then you can back substitute

25. Dido525

1 second.

26. Dido525

x₁=2.5+3.5t ?

27. Dido525

x₂=6-2t?

28. wio

yeah I'm getting that too

29. wio

did you try it?

30. Dido525

One attempt left :3 . Fingers crossed.

31. wio

you can double check it you know

32. Dido525

How?

33. wio

plug in each equation into the equations

34. Dido525

Assign a random number to t and see if it works?

35. wio

like, plug in t for x_3 and 6-2t for x_2 into the equations

36. wio

hmm actually I'm not quite sure how to double check it

37. wio

let me look at wolfram

38. Dido525

You can do this on wolfram? O_O .

39. wio
40. wio

wolfram agrees... it's just a matter of the stupid answer verify thing not being a wingspan

41. Dido525

THANKS!!! It's right :) .

42. wio

No problem. Matrix is your friend.

43. Dido525

I love Linear algebra <3 .