Homework Help: Find a basis for the subspace of M2,2

1. Sep 30, 2008

Xingconan

1. The problem statement, all variables and given/known data

3. The attempt at a solution
I don't really know how to do this, so I hope someone can give some hints or briefly tell me what I should do.

2. Sep 30, 2008

HallsofIvy

Well, a good start is to write
$$\left[\begin{array}{cc}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -1 & -1\end{array}\right]= \left[\begin{array}{cc}-1 & 0 \\ 1 & 1 \end{array}\right]$$

Multiply them out and get 4 equations relating a11, a12, a21, and a22. Are those equations independent? If not how many "independent" variables do you have (in other words, how many must you know in order to be able to calculate the others?).