Sums Of Subspaces Inclusion Ezclusion Principle For Subspaces Let 3 0 0 0 0 0 And Let L1 Span 1 (22.13 KiB) Viewed 16 times
Sums of Subspaces, Inclusion- Ezclusion Principle for Subspaces). Let 3 --0--0-0--0) --@)-- ) , , 0 and let L1 = Span(@,,2,, 2) and L2 = Span(6,5,6). (0) Find bases for L1 and L2 and the dimensions of Li and L2. (ii) Find a basis for the sum Li + Ly of L1 and Ly, and then the dimension of Li + L2. (iii) Use the Inclusion-Exclusion Principle for Subspaces to find the dimension of Lin L2.
Present your answers in a table of the following form Subproblem Answer(s) (i) (a) A list/set of vectors G ELi which form a basis for Li: < = .... = ..., dim(L1) = ... (b) a list /set of vectors de L2 which form a basis for L2: di = .... d= ... a dim(12) = ... (ii) A list /set of vectors ft E Li+L, which form a basis for L1 +L: fi = ........, dim(L1 + L2) = ... (iii) By (,ii) and by the Inclusion Exclusion Principle, dim(LinL2) = dim(L1) + dim(L2) - dim(L1 +L2) = ...
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