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 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.