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Midterm 1-Fall 2006

Midterm 1-Fall 2006 - AMS 510.01 Fall 2006 Midterm#1 Name...

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Unformatted text preview: AMS 510.01 Fall 2006, Midterm #1 Name: Student ID: Score: /100 ( + /15 bonus) 1. Indicate whether each of the following statements is true or false. n should be taken as any constant positive integer. (2 points each). (a) For any q, r ∈ C , if | q | = | r | , then q 2 = r 2 . (b) { (1 , 2 , 3) , (2 , 3 , 0) , (3 , , 0) } is a basis for R 3 . (c) For any A , B , C ∈ R n × n , if AB = AC = I , then B = C . (d) Every symmetric matrix is invertible. (e) The set of rational numbers, Q = { a b : a, b ∈ Z } , form a field ( Z is the set of integers). (f) Every matrix has a well-defined transpose. (g) { (1 + i, 0) , (0 , 1 + i ) } is a basis for C 2 . (h) For any ~u, ~v, ~w ∈ R n , if ~u · ~v = ~u · ~w , then ~v = ~w . (i) If U = { ~u i } is any basis of a vector space U , then ~u i · ~u j = 0, ∀ i 6 = j . (j) The linear span of any three vectors from R 3 is a three-dimensional vector space....
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Midterm 1-Fall 2006 - AMS 510.01 Fall 2006 Midterm#1 Name...

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