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Find the solution of the system whose augmented matrix is:

 

\(\begin{pmatrix} 1 & 2 & 0 & | & 2\\ 2 & 0 & 1 & | & 1\\ 3 & 2 & 1 & | & 3 \end{pmatrix}\)

gretzu  Jan 29, 2018
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Let us find the determinant of this system

 

1  2  0   1  2

2  0  1   2  0

3  2   1  3  2

 

( 0  + 6  + 0 )  - ( 0 + 2 + 4)

 

6  -  6  =  0

 

This indicates that we either have no solutions or infinite solutions

 

Gretzu, we could solve this with Gaussian elimination, but it seems easier to just use some Algebra

 

We  have

 

x  + 2y    = 2 ⇒  2y  =  2 - x    (1)   

2x  + z  =  1       ⇒  z  =  1 - 2x    (2)

3x + 2y + z  = 3      (3)

 

Sub (1) and (2)  into (3)   and we have that

 

3x + (2 - x)  + (1 - 2x)  = 3     simplify

 

3  =  3

 

This is always true....so we have infinite solutions

 

Holding x  constant  we have the solutions   {  x, (2 - x) / 2  , 1 - 2x }

 

    

cool cool cool

CPhill  Jan 29, 2018
edited by CPhill  Jan 29, 2018

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