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.

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) (Show Source): You can put this solution on YOUR website!
We know what to say when there's no solution.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If we add the first two equations we get , so .
Substituting that value, all three equations turn out to be .
Then, in terms of 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.

RELATED QUESTIONS
The system of equations may have a unique solution, an infinite number of solutions, or... (answered by Alan3354)
Please help me solve this problem: The system of equations may have a unique solution,... (answered by Alan3354)
Please help me this problem: The system of equations may have a unique solution, an... (answered by Alan3354)
The system of equations may have a unique solution, an infinite number of solutions, or... (answered by Alan3354)
The system of equations may have a unique solution, an infinite number of solutions, or... (answered by Edwin McCravy)
The system of equations may have a unique solution, an infinite number of solutions, or... (answered by AnlytcPhil)
Provide an example of a matrix that has no solution. Use row operations to show why it... (answered by MathLover1)
HAVING A 1) UNIQUE SOLUTION 2)AN INFINITE NUMBER OF SOLUTIONS 3)NO... (answered by Mathtut)
Trying to find a simple method of sovling the below linear equations for now and in the... (answered by josgarithmetic,MathTherapy)