Midterm 2-Fall 2007

Midterm 2-Fall 2007 - AMS 510.01 Fall 2007, Midterm #2...

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Unformatted text preview: AMS 510.01 Fall 2007, Midterm #2 Name: Student ID: Score: /100 ( + / 10 bonus) 1. Indicate whether each of the following statements is true or false. (2 points each). a) Every real matrix, A , can have an eigenvalue decomposition (given by = where D is diagonal). b) If we exchange rows 1 and 2 of A, the determinant of A will stay the same. c) Consider the transformation : defined by ( ) = (where A is an arbitrary matrix). F can be represented by a matrix, B , such that ( ) = . d) An real symmetric matrix always has m distinct real eigenvalues. e) lim = 1 . f) If lim = , then we can always find a number, N, such that | | > || for all > . g) sgn ({2, 4, 3, 1})= 0. h) If f is continuous at , then lim () = (lim ) . i) det 2 2 1 1 2 3 1 = 3 ....
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This note was uploaded on 02/09/2010 for the course AMS 510 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.

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Midterm 2-Fall 2007 - AMS 510.01 Fall 2007, Midterm #2...

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