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

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Dido525
 one year ago
Best ResponseYou've already chosen the best response.0I got x₁=5/2 x₂=6 x₃=t (free variable) The answer says I am wrong. Care to tell me what I did wrong?

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

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

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

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

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

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

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

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0when 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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