Question

Solve the following system by Gauss–Jordan elimination.

2x₁+5x₂+3x₃=35
12x₁+31x₂+20x₃=216

Answer 1

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?

Answer 2

@jim_thompson5910

Answer 3

@ParthKohli @UnkleRhaukus

Answer 4

x_3=0

Answer 5

Right. But whats wrong with my other answers?

Answer 6

Here is what the online page looks like:

Answer 7

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

Answer 8

What did were your elimination steps?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

Did you solve it like this?

Answer 15

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

Answer 16

I just added in the equation \(x_3=t\)

Answer 17

Sorry, that doesn't make sense.

Answer 18

I added in the equation: \[
0x_1+ 0x_2 +1x_3 = t
\]

Answer 19

Ohh I see.

Answer 20

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

Answer 21

So I do a back substitution?

Answer 22

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

Answer 23

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

Answer 24

then you can back substitute

Answer 25

1 second.

Answer 26

x₁=2.5+3.5t ?

Answer 27

x₂=6-2t?

Answer 28

yeah I'm getting that too

Answer 29

did you try it?

Answer 30

One attempt left :3 . Fingers crossed.

Answer 31

you can double check it you know

Answer 32

How?

Answer 33

plug in each equation into the equations

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

let me look at wolfram

Answer 38

You can do this on wolfram? O_O .

Answer 39

http://www.wolframalpha.com/input/?i=2x%2B5y%2B3z%3D35%2C+12x%2B31y%2B20z%3D216%2C+z+%3D+t

Answer 40

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

Answer 41

THANKS!!! It's right :) .

Answer 42

No problem. Matrix is your friend.

Answer 43

I love Linear algebra <3 .