Find a basis for each of the spaces and determine its dimension:
The space of all matrices A=[a b, c d] (2x2 matrix) in R^(2x2) such that a+d=0
The Attempt at a Solution
So I jumped at this question without knowing too much about spaces and dimensions, but:
I think a possible combination of basis can be: [1 0, 0 0]. [0 1, 0 0]. [0 0, 1 0] (not sure if [0 0, 0 -1] would be considered since d would be negative in this case) Also from that I assume the dimension is 3?
Truthfully even if I got it right, I do not even know what happened. Can someone conceptually tell me what I am doing exactly?
Thanks in advance.