(Matrices/Linear Systems) Find the solution of the system whose augmented matrix is...

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 }