NE112-practice-midterm-Fall-2009 -...

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Sample Midterm Questions for NE112 (Linear Algebra with Numerical Methods) Fall 2009 Question 1: Answer whether each statement is True (choose A) or False (choose B) (a) For every invertible n by n matrix A, there exists a nonzero n by n matrix B such that AB is the zero matrix. (b) If two invertible matrices A and B commute, then A -1 and B -1 must commute as well. (c) If A is a 3 by 3 matrix such that (A + I 3 ) 2 = 0, then A must be invertible. (d) The matrix is in row echelon form. (e) The matrix is similar to Question 2: The following system of equations has ____________________ solution(s).
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Unformatted text preview: (A)infinite (B)no (C)two (D)unique Question 3: Find all s and t so that B 2 = 0 if (A)There are no such s and t (B) t = 0 and s R (C) s = 0 and t = 0 (D) s = 0 or t = 0 (E) s = 0 and t R (F) s = 1 and t = -1 Question 4: If A , which one of the following statements is true for A-1 ? (A)The third row is [-1 -1 1] (B)The second column is [0 2 -1] T (C)The first row is [2 0 -1] (D)It does not exist (E)Each of B, C, D, and E are true (F) The second row is [1 2 -1] Solutions: 1) a) False b) True c) True d) False e) True 2) A 3) E 4) A...
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NE112-practice-midterm-Fall-2009 -...

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