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141Bquiz3c - 1 MATH 141B Print Name Instructor Dr Fabbri...

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1 MATH 141B Quiz#3 Date: Tues Feb 5, 2008 Print Name: Instructor: Dr. Fabbri [ 2 ] 1. Consider the matrix a - 1 1 0 1 - 2 a + 2 3 0 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 0 1 - 2 a + 2 3 0 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 0 1 0 - 1 0 1 a 0 , 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
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2 [ 2 ] 3. Consider the system of equations braceleftBigg 2 x + y - z = 1 3 x + y + 2 z = - 1 . Which of the following statements are true? i) The reduced row echelon form of the augmented matrix is bracketleftbigg 1 0 3 0 1 7 vextendsingle
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