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Unformatted text preview: ' is also idempotent. (b) Show that I − X ( X ' X ) − 1 X ' is idempotent as well. (c) Further, if X ' = (1 1 1 1 . .. 1) then show that I − X ( X ' X ) − 1 X ' reduces to I − 1 n 1 1' . 5. If X is any matrix (n x p) using the result that Tr(AB) = Tr(BA), show that Tr [ X ( X ' X ) − 1 X '] = p and deduce that Tr [ I − X ( X ' X ) − 1 X '] = n − p 6. For each of the system of equations below, determine how many solutions that each has, and explain your answer (you may do this using SPSS). (a) 3 x 1 − x 2 = 2 − 6 x 1 + 2 x 2 = − 4 (b) 2 x 1 − 3 x 2 = 5 − 2 x 1 + 3 x 2 = 2...
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 Fall '08
 KELLER
 Linear Algebra, Englishlanguage films, Following, Invertible matrix

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