reduce matrixs to row-ecelon form

Question

4x+3y-2z=6

2x+3y-4z=6

x-y+3z=-2

 

a) put the system into an augmented matrix

b)reduce into row-echelon form

c)solve the system

Answer 1

I haven't done linear algebra in some time, but I will give it a shot.

So your matrix will look like: 

|4    3    -2   |  6|

|2    3    -4   |  6|

|1   -1     3   | -2|

------------------------

Switch your row order, R₃ becomes R₁: 

 

|1  -1    3 |-2|

|2   3   -4 | 6|
|4   3   -2 | 6|

 

Now: R₂-2R₁ and R₃-2R₂

 

|1   -1     3 | -2|

|0    5   -10| 10|

|0   -3     6 | -6|

-------------------------

Now divide R₂ by 5:

 

|1   -1     3 | -2|
|0    1     -2|  5|
|0   -3     6 | -6|

-----------------------

R₃+3R₂:

 

|1   -1    3 | -2|
|0    1   -2 |  5|
|0    0    0 |  9 |

 

 

Since our last row is all 0's, except for the final entry, I believe that indicates there is no solution that will satisfy the system of equations.