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
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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
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