SOLUTION: <pre><b>Row echelon form of a system of linear equation is: 1 2 4 0 = 1 0 1 -1 2 = 2 0 0 1 3 = 0 0 0 0 1 = -2 a) write the system of equations corres

Algebra ->  Matrices-and-determiminant -> SOLUTION: <pre><b>Row echelon form of a system of linear equation is: 1 2 4 0 = 1 0 1 -1 2 = 2 0 0 1 3 = 0 0 0 0 1 = -2 a) write the system of equations corres      Log On


   

Question 316054: 
Row echelon form of a system of linear equation is:

1   2  4  0  =  1
0   1 -1  2  =  2
0   0  1  3  =  0
0   0  0  1  = -2

a) write the system of equations corresponding to this matrix.  us x1 x2 x3 x4 as variables.  

My answer: x1+2x2+4x3 = 1; x2-x3+2x4 = 2; x3+3x4 = 0; and x4= -2

b) determine whether the system is consistent or inconsistent.  if consistent, give the solution.  My answer:

from the equations above:
we know x4 = -2 so plug into
x3+3(-2)=0 solve for x3
    x3-6=0
      +6=0+6
      x3=6

we know x4=-2 and x3=6 plug into
x2-(6)+2(-2)=2
       x2-10=2+10
    x2-10+10=12
          x2=12

we know x4=-2; x3=6; x2=12 plug into
x1+2(12)+4(6)=1
     x1+24+24=1
           x1=-48+1
           x1=47

Can you let me know if this is correct?  If not please help me where I have it wrong.  Thank you!

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You look like you know what you're doing, but you made one slight typo on the last step. The last step should read x%5B1%5D=-47. Aside from that, everything else looks perfect. Because you are able to find a unique solution to the system, this means that the system is consistent and independent.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Everything's fine except the last step

x1=-48+1
x1=47 

The last step should be

x1=-47

You knew that. You just mistyped.

Edwin