+0

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

0
47
1
+266

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
Sort:

#1
+82489
+1

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 }

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

### 12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details