NE112-practice-midterm-Fall-2008

NE112-practice-midte - x y and z are variables and b is a real constant(W(X = = x y z 0x 2y 3z 0x = 3y bz(Y)Which of the following statements are

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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 - - 2 3 4 6 is invertible. F (c) Whenever a consistent system has free variables, the solution set contains many solutions. T (d) It is possible to multiply a 5-by-3 matrix by a length 5 column vector. F (e) The matrix 1 0 3 01 0 - 1 0 0 1 2 0 is in row echelon form. F Question 2: If A is a 3 x 3 matrix such that A01 = = 2 100 and A345 010 , then the product A678 is (A) 001 (B) (C) - 120 (D) (E) - 1 10 (F) (G) 91011 (H) (I) Answer is (B) (J) (K) (L) (M) (N) (O) (P) (Q) (R) (S) (T) Question 3: (U)

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(V)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, (W) (X) + + = + + = x y z 0x 2y 3z 0x + + = 3y bz (Y)Which of the following statements are true? (Z) 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. (AA) (A)II only (B) I and II only (C)I and III only (D)II and III only (E)I, II, and III (AB) (AC) Answer is (D) (AD) (AE) Question 4: (AF) (AG) (AH) If 111110101 , find the main diagonal of A-1 , (AI) (A) (0, 1, 0) (B) (-1, 0, -1) (C) (-1, -1, 1) (D) (0, -1, 0) (E) (-1, 0, 0) (AJ) (AK) Answer is E (AL) (AM)...
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This note was uploaded on 10/08/2010 for the course NE 112 taught by Professor Vanelli during the Spring '10 term at Waterloo.

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NE112-practice-midte - x y and z are variables and b is a real constant(W(X = = x y z 0x 2y 3z 0x = 3y bz(Y)Which of the following statements are

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