Sample Practice Midterm Questions_2007

Sample Practice Midterm Questions_2007 - (f) if a = -4 and...

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Practice Midterm Questions 2007 1. Answer whether each statement is True (choose #a) or False (choose #b) (i) A linear system must contain at least two linear equations (ii) Two linear systems are equivalent if and only if their associated augmented matrices are row equivalent. (iii) An nxn homogeneous linear system has a unique solution. (iv) Any two echelon forms for a given matrix A have the same number of zero rows. (v) If A = 6 4 2 1 , then A 2 - 7 A = 2 I 2 . (vi) If A is symmetric, then - A is skew symmetric. (vii) The equation A - 3 1 = - 1 . 3 5 . 4 is true for some matrix A with all nonzero entries. (viii) If A is a permutation matrix, then A k is a permutation matrix for every 2 k . 2. For which values of a and b does the system = + + = + - = + + - b az y x z x z y x 2 2 2 8 2 3 have more than one solution? (a) if a = -4 and b ≠ 0. (b) if a ≠ -4 and b ≠ 0. (c) if a = 4 and b = 0. (d) if a ≠ 4 and b ≠ 0. (e) if a = 4 and b ≠ 0.
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Unformatted text preview: (f) if a = -4 and b = 0. 3. Let A = --1 2 1 3 2 1 3 . then the main diagonal of A-1 is: (a) 1, 3, -7. (b) -1, -3, -6. (c) 1, -3, -7. (d) -1, 3, -6. (e) -1, -3, -7. (f) 1, 3, -6. 4. The lower triangular matrix [L] in the [L][U] decomposition of matrix given below = 33 23 22 13 12 11 32 31 21 1 1 1 22 12 8 16 8 10 4 5 25 u u u u u u is (a) 1 7333 . 1 32000 . 1 40000 . 1 (b) -2400 . 4 400 . 14 6 4 5 25 (c) 12 8 1 10 1 (d) 1 5000 . 1 32000 . 1 40000 . 1...
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Sample Practice Midterm Questions_2007 - (f) if a = -4 and...

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