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.
 Fall '08
 Staff

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