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# quiz2 - Quiz 2 Math 240 Calculus III February 3 2009 Name...

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Quiz 2 Name: Math 240 - Calculus III February 3, 2009 Note: In order to receive full credit, you must show work that justiﬁes your answer. 1. Find the inverse of the matrix A = 1 0 1 0 1 1 1 1 0 . Solution : 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 - 1 - 1 0 1 clear ﬁrst column 1 0 1 1 0 0 0 1 1 0 1 0 0 0 - 2 - 1 - 1 1 clear second column 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 2 1 2 - 1 2 obtain 1 in lower right 1 0 0 1 2 - 1 2 1 2 0 1 0 - 1 2 1 2 1 2 0 0 1 1 2 1 2 - 1 2 done! Therefore, A - 1 = 1 2 1 - 1 1 - 1 1 1 1 1 - 1 . 2. Find all eigenvalues and at least one eigenvector of the matrix B = ± 1 3 4 2 ² . Solution : The eigenvalues are the numbers λ that satisfy det( B - λ I ) = 0. det( B - λ I ) = ³ ³ ³ ³ 1 - λ 3 4 2 - λ ³ ³ ³ ³ = (1 - λ )(2 - λ ) - 12 = λ 2 - 3 λ - 10 = ( λ - 5)( λ + 2) So λ = - 2 and λ = 5 are the eigenvalues.

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quiz2 - Quiz 2 Math 240 Calculus III February 3 2009 Name...

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