# Matrix solution question.

• Jan 25th 2010, 08:24 PM
Planeman
Matrix solution question.
I am supposed to say if the following matrix has no solutions, a unique solution, or infinitely many.
[1 -2 2 -3 0
2 -4 5 -4 0
2 -4 4 -6 0
1 -2 1 -5 0]

I reduced this and got this matrix:

[1 -2 2 -3 0
0 0 1 2 0
0 0 1 2 0
0 0 0 0 0]

The two identical equations would just reduce to one equation so I am left with 4 unkowns and two equations. I know you can describe the solutions parametrically using s & t but is that what I would do in this situation?

Any help would be appreciated. Thank You
• Jan 25th 2010, 11:20 PM
Prove It
Quote:

Originally Posted by Planeman
I am supposed to say if the following matrix has no solutions, a unique solution, or infinitely many.
[1 -2 2 -3 0
2 -4 5 -4 0
2 -4 4 -6 0
1 -2 1 -5 0]

I reduced this and got this matrix:

[1 -2 2 -3 0
0 0 1 2 0
0 0 1 2 0
0 0 0 0 0]

The two identical equations would just reduce to one equation so I am left with 4 unkowns and two equations. I know you can describe the solutions parametrically using s & t but is that what I would do in this situation?

Any help would be appreciated. Thank You

Since your parameters can take on infinitely many values, surely there must be infinitely many solutions.