Originally Posted by

**Lord Darkin** Hello,

I have a question that's asking me if a set of four 3x1 matrices are a spanning set of R^3 (the entire 3-D space)..

So I have to figure out how to represent them in a linear combination with 4 different variables that I call alpha1 - alpha4. If the system's inconsistent, then I know that the set of 4 matrices is not a spanning set of R^3. I'm stuck at the following matrix:

1 0 0 0 -- a + b - c

0 1 0 2 -- b

0 0 1 1 -- -b + c

Where $\displaystyle [a,b,c]^T$ represents the idea that any 3x1 matrix can be written as a linear combination of the 4 matrices that were given in the problem.

My concern is that I'm stuck at the matrix I wrote above, and am not sure at how to continue. **It's not in reduced row echelon form, and I'm not sure how to get it in that kind of form.**