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Find explicit rules for the following recursive sequences:
a) an = 2(anâ1) + 4;a1 = 5
b) an = 6(anâ1)â8(anâ2);a1 = 1,a2 = 0
Please be thorough and explanation all steps.
Show, for a positive integer n, that F^n = W_1âW_2, where W_1 and W_2 are the following subspaces of F^n:
W_1 ={(a1,...,an) â Fn | an = 0}
W_2 ={(a1,...,an) â Fn | a1 = a2 = ··· = anâ1 = 0}.