Exam 2 Solution

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online