141Bquiz3c - 1 MATH 141B Quiz#3 Date: Tues Feb 5, 2008...

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Unformatted text preview: 1 MATH 141B Quiz#3 Date: Tues Feb 5, 2008 Print Name: Instructor: Dr. Fabbri [ 2 ] 1. Consider the matrix a- 1 1 1- 2 a + 2 3 a , where a is a real number. Which of the following statements are true? i) det A = 2 a 2 + 4 a + 6 . ii) A is an invertible matrix if a = 1 , but not if a =- 1. iii) If a = 2 then the system of equations a- 1 1 1- 2 a + 2 3 a x y z = b 1 b 2 b 3 has a solution for every choice of b 1 , b 2 and b 3 . A) i) and ii) only, B) i) and iii) only, C) ii) and iii) only, D) i) only, E) all true [ 2 ] 2. Consider the matrix 1 1- 1 0 1 a , where a is a real number. Which of the following state- ments are true? i) det A = 1 + a. ii) A is an invertible matrix for every value of a . iii) ( A- 1 ) 32 = a. A) none true, B) ii) only, C) i) and ii) only, D) i) and iii) only, E) ii) and iii) only 2 [ 2 ] 3. Consider the system of equations braceleftBigg 2 x + y- z = 1 3 x + y + 2 z =- 1 ....
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141Bquiz3c - 1 MATH 141B Quiz#3 Date: Tues Feb 5, 2008...

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