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141Bquiz4c

# 141Bquiz4c - 1 MATH 141B Quiz#4 Date Mon Instructor Dr...

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1 MATH 141B Quiz#4 Date: Mon Feb 12, 2008 Instructor: Dr. Fabbri [ 2 ] 1. Consider the matrix A = bracketleftbigg - 3 2 1 - 4 bracketrightbigg . Which of the following 3 statements are true? i) A has characteristic equation r 2 - 7 r + 10 = 0 . ii) A has two distinct eigenvalues. iii) v = bracketleftbigg - 1 1 bracketrightbigg is an eigenvector with eigenvalue - 5 . 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 A = 3 0 - 2 0 2 1 - 2 0 3 . Which of the following 3 statements are true? i) A has three distinct positive eigenvalues. ii) The largest eigenvalue of A is r = 2 . iii) v = - 3 1 3 is an eigenvector corresponding to the largest eigenvalue. A) i) and ii) only, B) i) and iii) only, C) ii) and iii) only, D) i) only, E) all true

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2 [ 2 ] 3. Suppose that a matrix A has eigenvalues r 1 = 5 and r 2 = 1 with corresponding eigenvectors v 1 = bracketleftbigg - 1 3 bracketrightbigg and v 2 = bracketleftbigg 1 1 bracketrightbigg . If w = bracketleftbigg - 5 7 bracketrightbigg , then find the y -coordinate of A 10 w .
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141Bquiz4c - 1 MATH 141B Quiz#4 Date Mon Instructor Dr...

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