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exam1p - MA 527 PRACTICE EXAM 1 Fall 2000 NAME STUDENT ID 1...

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MA 527 PRACTICE EXAM 1 Fall 2000 Page 1/5 NAME STUDENT ID 1. Defne A = 1 4 7 2 5 8 3 6 9 . (a) By using row operations, determine i± A is singular or nonsingular. (b) What is the rank o± A ? (c) Solve the set o± equations A x 1 x 2 x 3 = 0 0 0 .

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MA 527 PRACTICE EXAM 1 Fall 2000 Page 2/5 For the problems on this page, you need not show any work. Circle the correct answers. (5) 2. Which of the following statements are true? i) If Ax = b has 2 di±erent solutions, then the homogeneous system Ax = 0 must have in²nitely many solutions. ii) If ˜ A is obtained from a matrix A by row operations, then rank ˜ A =rank A . (5) 3. Which of the following are vector spaces? i) The set of all vectors ( a 1 ,a 2 3 ) such that a 2 1 - a 2 2 = 0. ii) The set of all vectors ( a 1 2 3 ) such that a 1 - a 2 = 0. (5) 4. Which of the following are correct statements? i) If A is a real symmetric matrix, then all of its eigenvalues are real. ii) Eigenvectors corresponding to di±erent eigenvalues are linearly independent.

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