- #1

- 185

- 4

## Homework Statement

Write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or infinitely many solutions.

-x+y-z=4

x-y+2z=3

2x-2y+4z=6

## Homework Equations

## The Attempt at a Solution

I saw right away that Row 3 and Row 2 are the same equation, off by a factor of 2. Because of this, I was able to make the matrix with a zero row for Row 2, which shows that row 2 and row 3 are linearly dependent. However, my question arises here. I know that a zero row and linear dependence of these two equations means that there is either 0 solutions or infinitely many solutions. Since they are linearly dependent, there is not one unique solution. However, How can I tell whether there is 0 solutions or infinitely many?