SOLUTION: The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists.

Algebra ->  Matrices-and-determiminant -> SOLUTION: The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists.       Log On


   

Question 1108690: The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.)

x + y + z = 0
8x − y − z = 0
−x + 8y + 8z = 0
(x, y, z) =?

Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
We know what to say when there's no solution.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If we add the first two equations we get 9x=0 , so x=0 .
Substituting that value, all three equations turn out to be y%2Bz=0 .
Then, in terms of z, y=-z .
The infinitely many solutions are (0,-z,z).
Why would we want to use matrices,
when the solution jumps at you
without any effort on your part.