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e-hm-lina.2011t

# e-hm-lina.2011t - Linear Alg MAS4105 Due By Optional...

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Linear Alg MAS4105 Optional Project-E Prof. JLF King 5Dec2011 Due: By 10AM , on Monday, 12Dec2011. E1: Short answer: Show no work. Please write DNE in a blank if the described object does not exist or if the indicated operation cannot be performed. a Markov digraph has states A, B . The transition-probs are: P ( A A ) := s , P ( A B ) := c , P ( B A ) := 1, where s,c [ 0 , 1 ] with s + c = 1. With M c the M.M., the ( unique ) probvec v c satisfying M c v c = v c is v c := . . . . . , . . . . . t , ITOf c . Whence M.process X 0 X 1 . . . with Distr( X 0 )= v c , and cond.-distr Distr( X n +1 | X n ) given by M c . The prob that X 0 X 1 X 2 X 3 = AABA is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b In R 4 , let L 1 be the line passing through the origin and the point Q := (1 , 2 , 3 , 4). Let L 2 be the line t 7→ (2 , - 1 , 0 , 1) - t · (5 , 0 , 1 , 2). The ( orthogonal ) dist. between lines L 1 and L 2 is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The closest-points are c 1 = . . . . . . . . . . . . . . . . . . . . . . . . . . and c 2 = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ Hint: Use the method from the skew-line essay question. ] Essays Your 2 Essays must be typed , and double or triple spaced. Use the Print/Revise cycle to produce good, well thought out, essays. Start each essay on a new sheet of paper. Do not restate the problem; just solve it.
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