Find the basis and it's dimension
Find a basis for
W = {a b
_____c d
:a+d=b+c} and state the dimension of W.
Showing my work:
I thought one way to solve this would be to exhange values in the matrix:
Then establish our vector set. Determine if the set spans for W. We then show linear independence...and therefore our basis.
Problem is:
I set up matrices like this:
a 1 0 +b0 0 c0 0 +d0 1
...1 0....0 0...0 0....0 1
I then took a+b=c+d
and said: ac=db
Anyway, some years ago I did some similar math and thought of this:
Wy not replace
a b
c d
with:
a a
e e
I used e is epsilon. Please feel free to trash my "thought" process and do not follow my example to solve it as it need not be solved this way, that is: I am just trying what I remember from previous years.
You could say I am kind of grapsing at straws here guys (and gals) and need some help!
Please advise,
Thanks.
