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11 Nov 2019
4. (Intersection of Subspaces, Inclusion-Ezclusion Principle for Sabupaces). Let the vectors a, , a and , and their linear spans 1_ Span(": "gos) and L2-Span(5, be the same as in Problem 1. ) Represent each of L1 and L2 as the solution set of a suitable homogeneous linear system. (i) Use (i) to find a basis for the intersection L1 n L2 of L1 and L2 and the dimension of L n L (ili) Use (il) and the Inclusion-Exclusion Principle for Subspaces to find (again) the dimension of L.+2
4. (Intersection of Subspaces, Inclusion-Ezclusion Principle for Sabupaces). Let the vectors a, , a and , and their linear spans 1_ Span(": "gos) and L2-Span(5, be the same as in Problem 1. ) Represent each of L1 and L2 as the solution set of a suitable homogeneous linear system. (i) Use (i) to find a basis for the intersection L1 n L2 of L1 and L2 and the dimension of L n L (ili) Use (il) and the Inclusion-Exclusion Principle for Subspaces to find (again) the dimension of L.+2