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

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Dido525 Group TitleBest ResponseYou've already chosen the best response.0
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?
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
@jim_thompson5910
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
@ParthKohli @UnkleRhaukus
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
x_3=0
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Right. But whats wrong with my other answers?
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Here is what the online page looks like:
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
Shouldn't the other variables be in terms of the free variable?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
What did were your elimination steps?
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
It's difficult to post the elimination steps here. I checked with my calculator though. It's correct.
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
But yeah, that's what I think @wio . I don't know how to express it though.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
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
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
but t is a free variable is it not? SO it can be any value it wants.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
\[ \begin{bmatrix} 2&5&3 \\ 12&31&20 \\ 0&0&1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 35 \\ 216 \\ t \end{bmatrix} \]
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
Did you solve it like this?
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
No... How did you get 0,0 and 1?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
I just added in the equation \(x_3=t\)
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Sorry, that doesn't make sense.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
I added in the equation: \[ 0x_1+ 0x_2 +1x_3 = t \]
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Ohh I see.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
All of the elimination you did before should work for the most part.
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
So I do a back substitution?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
You first want to get the second row to have a zero in it's first colum
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
because x3=t so solve the others n terms of t.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
then you can back substitute
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
x₁=2.5+3.5t ?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
yeah I'm getting that too
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
did you try it?
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
One attempt left :3 . Fingers crossed.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
you can double check it you know
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
plug in each equation into the equations
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Assign a random number to t and see if it works?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
like, plug in t for x_3 and 62t for x_2 into the equations
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
hmm actually I'm not quite sure how to double check it
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
let me look at wolfram
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
You can do this on wolfram? O_O .
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
http://www.wolframalpha.com/input/?i=2x%2B5y%2B3z%3D35%2C+12x%2B31y%2B20z%3D216%2C+z+%3D+t
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
wolfram agrees... it's just a matter of the stupid answer verify thing not being a wingspan
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
THANKS!!! It's right :) .
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.3
No problem. Matrix is your friend.
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
I love Linear algebra <3 .
 one year ago
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