Thread: help needed with a proof

Suppose that

M={(a b ;a,b,c belong to R
-b c)

and N={(x 0 ;x,y belong to R
y 0)

are subspaces of M2R. Show that (M:R) + (N:R) = ((M'intersect'N):R) + ((M+N):R)

Cheers, Shaun

Originally Posted by Shaun Gill

Suppose that

M={(a b ;a,b,c belong to R
-b c)

and N={(x 0 ;x,y belong to R
y 0)

are subspaces of M2R. Show that (M:R) + (N:R) = ((M'intersect'N):R) + ((M+N):R)

Cheers, Shaun

I presume,

This looks like the principle of inclusion-exlusion.
Thus,

Thus,

So dimensions are,

I believe that is the idea.

But the sad thing is I do not know how to generalize this to infinite fields. So far this confirms what you said for finite fields.

I think that these are the same problem.
http://www.mathhelpforum.com/math-he...ons-basis.html