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

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

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

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

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

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

Dido525
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.3Did you solve it like this?

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

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

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

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

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

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

wio
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0because x3=t so solve the others n terms of t.

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

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

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

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

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

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

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

wio
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0THANKS!!! It's right :) .

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

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