Given this augmented matrix $$\left[\begin{matrix}1 & -5 & 4 & -3 \ 2 & -7 & 3 & -2 \ -2 & 1 & 7 & -1\end{matrix}\right]$$ Is the answer "no solution"?

I multiplyed row 3 by 1 and added to 2. Then row times 2 and added to row 3. Then I did row 2 times (-3/2) and added to 3, but that gave me a row with 0 0 0 -23/2.
So, did I do this right? And, if so, does this imply there is no solution?

Question

Given this augmented matrix $$\left[\begin{matrix}1 & -5 & 4 & -3 \ 2 & -7 & 3 & -2 \ -2 & 1 & 7 & -1\end{matrix}\right]$$ Is the answer "no solution"?

I multiplyed row 3 by 1 and added to 2. Then row times 2 and added to row 3. Then I did row 2 times (-3/2) and added to 3, but that gave me a row with 0 0 0 -23/2. 
So, did I do this right? And, if so, does this imply there is no solution?

anonymous · Answer

The second step should say row 1 times 2 and added to row 3.

anonymous · Answer

Any thoughts on this one guys? I could use a second opinion

hartnn · Answer

yes, now even i get no solution, by different set of row/column operations.

anonymous · Answer

Ok good! It was the second time it has happened on this problem, but the first time since I learned this in class that Ive encountered it and wanted to be sure. Thanks for taking a look!

hartnn · Answer

no prob, welcome ^_^