Solving a System of Equations with Matrices

[elle]

Hi, I've just been given a set of revision questions for matrices and I'm having problems with the following question:

http://tinypic.com/ejbssz.jpg"

My task is to find the general solution of this system (if there is any). Do I start off by reducing it to row echelon form and then reduced row echelon?

My first step would be to divide the first line by 3 to get a 1 on the far left...but that would mean I would have fractions as well which makes everything so 'messy.' Is that the correct first step to this question?

Help and advice appreciated! Thank you!

 

[happyg1]

I would start by multiplying the 2nd line by -1 and adding it to the 4th line.

 

[elle]

Ok I've given it a go and I got the answer:

1 0 1 2 | 1
0 1 -1 -2 | 0
0 0 0 0 | 0
0 0 0 0 | 0

So that gives me no solution?... Can someone check if that's right. Thank you!

 

[enigma]

Looks correct to me. The matrix is singular, so there isn't a solution.

 

[elle]

Oh thanks! I know how to attempt other similar questions in my notes now.

I've also got two more questions to ask, if that's ok

1) How do you determine a matrix is an elementary matrix? For example if you were given:

1 0 0
0 1 9
0 0 1

Is this an elementary matrix?

2) I don't understand the wording of the following question:

http://tinypic.com/ejek4w.jpg"

Does it mean its already in the echelon form so I don't have to do anything apart from just solving it for the variables? Or do I still have to put it into reduced echelon form?

Sorry for being such a pain and thank you for taking time to read my post