Determine a solution to each of the following linear systems. using the fact that Ax = h is consistent if and only if h is a linear combination of the columns of A: (, ) (b)

Notes Revision 1 ● Subset of a set ○ x327/x3 = (x9)(x^2+9x) ○ x^38/x2=(x2)(x^2+4x+2)/(x2) ● Set under consideration in a problem ○ ex: 2 sets u= {1,2,4,7,9}, a= {2,4,7}, a1= {1,9} ● The complement to set A, when in A1 in the set Abut in U but not in A ● Operations on sets: union of 2 sets A and B, written aB, in the set A as in set B or in both sets A and B ○ ex: A={a,b,c}, B={f,g}, P={a,b,c,f,g,hB={a,b,c,f,g} ○ Intersection of sets A and B. The sets of elements that belong to both A and B. Symbolically then in written asB. ○ ⋃union, uuniversal,intersection ○ ex: A={1,2,3,5}, B={1,2}, B={1,2} Let A={1,2,4,5,}, B={4,1,3,7,8}B={1,4} Find (1) AA1 u={1,23,4} A={2,3} A1={1,4} (2) A⋃ ϕ=A (3) A⋂ ϕ=ϕ ● Disjoint sets 2 Sets A and B are disjoints if and onlB=iϕ A⋂ ○ Disjoint is when A and B have nothing in common, not disjoint is when they do have something in common.