Did My Matrix Calculations Lead to the Correct Solution?

[elle]

I've been asked to solve the following matrix and find the solutions but I'm not sure if I've reached the correct 'end' matrix.

Original matrix:

1 2 -1 3
-1 3 4 10
-1 1 -2 8

The last matrix I got after my calculations:

1 2 -1 3
0 1 1 11/3
0 0 8 26/3



Thanks for reading

 

[HallsofIvy]

What do you mean by "solving" a matrix? I know how to solve equations and I know, more generally, how to solve problems but I don't know what is meant by solving a matrix.
You appear to be row-reducing a matrix to row-echelon form. If so that is certainly not what I get. How about stating exactly what the problem is and showing your work?

 

[elle]

oh its okay, I've managed to work out where I went wrong. Sorry for not stating the problem clearly

Erm but I have two more questions to ask, and was wondering if anyone can offer me some help or hints. I haven't got any working for this because I really do not have any idea how to approach the answer.

Can anyone explain to me what a subspace is? I've got notes on it but I'm confused with all the notation etc. Thanks in advance!

http://tinypic.com/f1mp3b.jpg"

 

[hypermorphism]

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Can anyone explain to me what a subspace is?
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A subspace of a vector space is just a subset of the vectors in the space that are also a vector space. For example, R² is a 2-dimensional vector space. The set of vectors (x,y) that satisfy the equation y=x is a subspace of R² but the set of vectors (x,y) that satisfy x² + y² = 1 is not.