Solving Matrix with Gaussian Elimination: Find Solutions

[Firepanda]

I used Gaussian elimination on a matrix to find the soultions. I know that there is either no solutions or infinatley many, but the matrix is confusing me.

The only definition I have of when a matrix has infinatley many solutions is when a zero row is equal to zero, and no solutions when a zero row is equal to a real number.

But in this case is it infinatley many solutions or no solutions?

1 2 3 | 4

0 3 1 | 1

0 3 1 | 0

Where 3y + z = 1 and 0.

Thanks

 

[HallsofIvy]

I used Gaussian elimination on a matrix to find the soultions. I know that there is either no solutions or infinatley many, but the matrix is confusing me.

The only definition I have of when a matrix has infinatley many solutions is when a zero row is equal to zero, and no solutions when a zero row is equal to a real number.

0 is a real number! You mean a non-zero number.

But in this case is it infinatley many solutions or no solutions?

1 2 3 | 4

0 -3 -1 | -1

0 -3 -1 | 0

Where -3y - z = -1 and 0.

Thanks

You haven't finished your Gaussian Elimination. Subtract the second row from the third.

 

[mjsd]

your matrix is not in reduced-echelon form yet. do row 2 minus row 3 and see...

 

[Firepanda]

ah, so no solutions :P thanks