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NE112-practice-midterm-Fall-2008_and_solutions-

# NE112-practice-midterm-Fall-2008_and_solutions- - x y and z...

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Sample Midterm Questions for NE112 (Linear Algebra with Numerical Methods) Fall 2008 Question 1: Answer whether each statement is True (choose #a) or False (choose #b) (a) If matrices A and B “commute'” this implies that AB - BA= 0. T (b) The matrix is not invertible. T (c) Whenever a system has free variables, the solution set contains many solutions. (d) It is possible to multiply a 5-by-3 matrix by a length 5 column vector. F (e) The matrix is in row echelon form. F Question 2: If A is a 3 x 3 matrix such that , then the product is (A) (B) (C) (D) Answer is (B)

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Question 3: Consider the following system of linear equations over the real numbers, where
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Unformatted text preview: x , y , and z are variables and b is a real constant, Which of the following statements are true? I. There exists a value of b for which the system has no solution. II. There exists a value of b for which the system has exactly one solution. III. There exists a value of b for which the system has more than one solution. (A)II only (B) I and II only (C) I and III only (D)II and III only (E) I, II, and III Answer is (D) Question 4: If , find the main diagonal of A-1 , (A) (0, 1, 0) (B) (-1, 0, -1) (C) (-1, -1, 1) (D) (0, -1, 0) (E) (-1, 0, 0) Answer is E...
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