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11 Nov 2019
2. (Sums of Subspaces, Inclusion-Ezclusion Principle for Subspaces). Let and b-6 and let L1Span(a, a) and 2 Span(6, (1) Find bases for L1 and 1,2 and the dimensions of Ly and 12. (ii) Find a basis for the sum Li + L2 of L1 and L2, and then the dimension of L1 + L2. (ili) Use the Inclusion-Exclusion Principle for Subepaces to find the dimension of La nL (lv) Verify your results in () and (ii) with Wla by entering the following commands one by one: spanC (1,-2,1,-2), 1,-3, 1,1), (-1,1,-3,3)) span( (-2,2,-6,6), (1,-1,3,-2), (-1,1,-3,4)) spanc (1,-2,1,-2), (1,-3.-1,-1). (-1,1,-3,3),(-2,2,-6,5),(1.-1,3,-2), (-1,1,-3,4) (each time consult the Diseneion part of the answer produced by Wlo.
2. (Sums of Subspaces, Inclusion-Ezclusion Principle for Subspaces). Let and b-6 and let L1Span(a, a) and 2 Span(6, (1) Find bases for L1 and 1,2 and the dimensions of Ly and 12. (ii) Find a basis for the sum Li + L2 of L1 and L2, and then the dimension of L1 + L2. (ili) Use the Inclusion-Exclusion Principle for Subepaces to find the dimension of La nL (lv) Verify your results in () and (ii) with Wla by entering the following commands one by one: spanC (1,-2,1,-2), 1,-3, 1,1), (-1,1,-3,3)) span( (-2,2,-6,6), (1,-1,3,-2), (-1,1,-3,4)) spanc (1,-2,1,-2), (1,-3.-1,-1). (-1,1,-3,3),(-2,2,-6,5),(1.-1,3,-2), (-1,1,-3,4) (each time consult the Diseneion part of the answer produced by Wlo.
Jarrod RobelLv2
25 Aug 2019