Dido525
Solve the following system by Gauss–Jordan elimination.
2x₁+5x₂+3x₃=35
12x₁+31x₂+20x₃=216
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Dido525
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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?
Dido525
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@jim_thompson5910
Dido525
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@ParthKohli @UnkleRhaukus
UnkleRhaukus
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x_3=0
Dido525
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Right. But whats wrong with my other answers?
Dido525
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Here is what the online page looks like:
wio
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Shouldn't the other variables be in terms of the free variable?
wio
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What did were your elimination steps?
Dido525
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It's difficult to post the elimination steps here. I checked with my calculator though. It's correct.
Dido525
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But yeah, that's what I think @wio . I don't know how to express it though.
UnkleRhaukus
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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
Dido525
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but t is a free variable is it not? SO it can be any value it wants.
wio
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\[
\begin{bmatrix}
2&5&3 \\
12&31&20 \\
0&0&1
\end{bmatrix}
\begin{bmatrix}
x_1 \\ x_2 \\ x_3
\end{bmatrix}
=
\begin{bmatrix}
35 \\ 216 \\ t
\end{bmatrix}
\]
wio
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Did you solve it like this?
Dido525
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No... How did you get 0,0 and 1?
wio
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I just added in the equation \(x_3=t\)
Dido525
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Sorry, that doesn't make sense.
wio
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I added in the equation: \[
0x_1+ 0x_2 +1x_3 = t
\]
Dido525
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Ohh I see.
wio
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All of the elimination you did before should work for the most part.
Dido525
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So I do a back substitution?
wio
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You first want to get the second row to have a zero in it's first colum
Dido525
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because x3=t so solve the others n terms of t.
wio
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then you can back substitute
Dido525
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1 second.
Dido525
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x₁=2.5+3.5t ?
Dido525
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x₂=6-2t?
wio
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yeah I'm getting that too
wio
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did you try it?
Dido525
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One attempt left :3 . Fingers crossed.
wio
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you can double check it you know
Dido525
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How?
wio
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plug in each equation into the equations
Dido525
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Assign a random number to t and see if it works?
wio
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like, plug in t for x_3 and 6-2t for x_2 into the equations
wio
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hmm actually I'm not quite sure how to double check it
wio
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let me look at wolfram
Dido525
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You can do this on wolfram? O_O .
wio
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wolfram agrees... it's just a matter of the stupid answer verify thing not being a wingspan
Dido525
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THANKS!!! It's right :) .
wio
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No problem. Matrix is your friend.
Dido525
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I love Linear algebra <3 .