Test_1-QA

Test_1-QA - MATH1111/29Sept10 1 THE UNIVERSITY OF HONG KONG...

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MATH1111/29Sept10 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS Linear Algebra Part I [ 2 marks for correct answer, ± 1 2 mark for wrong answer, 0 mark for no answer ] 1. Let ± 6 = 0 and A = 0 @ ± 1 1 1 0 1 1 0 0 ± ± 1 A . Which of the following is/are true? (i) det A = ± (ii) A ± 1 = 0 @ ± 1 ± 1 0 0 1 ± 1 0 0 ± ± 1 A (iii) The (1 ; 1)th entry of A 2010 is 1. A. (i) only B. (i) and (ii) only C. (i) and (iii) only D. all of them E. none of A,B,C,D C 2. Consider the systems (a) 8 < : x ± y + z ± 3 w = 3 3 x + y ± z ± w = 1 2 x ± y ± 2 z ± 4 w = 1 and (b) 8 < : 2 x + y ± z + w = 2 x ± y + 2 z + w = 1 4 x ± y + 3 z + 3 w = 3 Which below is true? A. Both systems are inconsistent. B. System (a) has two free variables. C. Systems (a) and (b) are equivalent. D. System (a) has exactly one solution with w = 1. E. None of A;B;C;D . D
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MATH1111/29Sept10 2 3. Let A and B be 2 ± 3 matrices. Applying the following elementary row operations in order: i) R 1 $ R 2 , ii) ² 2 R 1 + R 2 , iii) 2 R 2 + R 1 , iv) ² R 2 , the matrix A is reduced to B . Find a matrix E such that EA = B .
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Test_1-QA - MATH1111/29Sept10 1 THE UNIVERSITY OF HONG KONG...

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