SOLUTION: For the matrix given in RREF, write the solution of the system of equations. [1 2 | 1] [0 0 | 0]

Algebra ->  Matrices-and-determiminant -> SOLUTION: For the matrix given in RREF, write the solution of the system of equations. [1 2 | 1] [0 0 | 0]      Log On


   

Question 1199571: For the matrix given in RREF, write the solution of the system of equations.
[1 2 | 1]
[0 0 | 0]
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

For the given RREF, the standard form of the system of linear equations is

    1x + 2y = 1,

    0x + 0y = 0.


The second equation is always valid for any values of x and y. 
Therefore, it does not carry any information and we can neglect it.


So, we have, actually, only one working equation

    x + 2y = 1.


It means that y can be any value, and x = 1 - 2y.


ANSWER.  y can be any value and x = 1-2y  is the general solution.

Solved and explained.