For are a 1 3 b 1i 1 i c 2 3 d 2i 2 i e 2i

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Unformatted text preview: 2 5 4 5 8 7 2 5 , 4 1 1 2 , 1 3 2 6. Which of the following sets is a basis for the set of all vectors of the form ,,, ? 3 a) 1 2 , 1 3 e) 1 2, 1 7. Let 2 5 , 4 1 2 5, 4 : 5 8 7 1 , 2 5 4 1 b) 5 8, 7 f) 5 8 7 1 , , c) , g) e) k = 50, cos b) k = 5, cos 1/2, 1, x c) k = 50, cos f) k = -5, cos 1, g) k = x, where 1, d) k = 5√2, cos √, √ h) k = 5, cos , √2 8. Which of the following sets is a subspace of a) 2 5 4 2 5 8 7 : ,, b) ? : 2 :, c) 3 d) : , 5 5 . The action 5 5 around the origin, followed with multiplication by a of on consists of a rotation by an angle scalar, . Find the scalar and cos . 1, d) 1000 0100 , , , 0010 0001 be the linear transformation given by a) k = 5, cos , 5 8 7 1 ,, e) :5 6 0 1/2 Part III. 3 31 1 1. [12 pts] The matrix 0 2 0 has an eigenvector 0 . Also, 2 is an eigenvalue of . 2 60 2 Diagonalize by constructing appropriate matrices and writing the matrix equation that relates these matrices with . 1 0, 2 For v For 2: 1 0 so 2 v is 1 0 2 3 0 6 has corresponding eigenvalue 1 1 1 ~0 0 2 0 or x 31 0 0 so 00 3 and corresponding eigenvectors are 1 and 0 3 3 1 0 1...
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This note was uploaded on 01/17/2014 for the course ESE 309 taught by Professor Staff during the Fall '08 term at Washington University in St. Louis.

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