2JMidtermPractise

# 2JMidtermPractise - A = 1 1 1 3 5 6-2 2 7 b What is det...

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Practise Midterm Exam - Linear Algebra and Infinite Series Math 2J, Fall 2008 Date: 10/28/08 Name: (1) You have 60 minutes to complete the test. 1

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(1) (20 pts) a) Let A = 1 0 1 3 3 4 2 2 3 Find A - 1 . b) Solve the linear system x 1 + x 3 = 5 3 x 1 +3 x 2 +4 x 3 = 2 2 x 1 +2 x 2 +3 x 3 = 1
(2) (20 pts) Consider the following linear system of equations: - x 1 - x 2 +2 x 3 = 7 x 1 + x 2 - x 3 = 5 - x 3 + x 4 = 3 x 1 - x 4 = 1 Use Cramer’s rule to ﬁnd x 3 .

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(3) (20 pts) a) Compute the LU factorization of the following matrix:

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Unformatted text preview: A = 1 1 1 3 5 6-2 2 7 b) What is det( A )? (4) (20 pts) Suppose that a certain 3 × 3 matrix A has real eigenvalues. You know that det( A ) = 2 and Tr( A ) = 0. You also know that two of the eigenvalues of A are equal. Find the eigenvalues of A . (5) (20 pts) Let A be the matrix ± 3 2-1 0 ² . Find A 50 ....
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2JMidtermPractise - A = 1 1 1 3 5 6-2 2 7 b What is det...

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