We have a system of 3 linear equations with 4 variables, does it always have a solution? (homework)
In example we have this matrix (after the row reduction process):
1 0 0 -335/21 0 1 0 2596/147 0 0 1 -104/147
All of the 3 linear equations are equal to 0.
The 1st equation is this: $x+ 0y + 0z + (-335/21)w = 0$ So the solution to this system is:
w ( 335/21, -2596/147, 104/147, 1)
So the system, has infinite solutions?
But what is the answer to the question (in title)?
(We have to say if it's true/ false, and why)
I believe it's false as in general a system of linear equations can have infinite solutions, or 1 unique or none..is that correct?
Thank you for your time!