Published on 31 Jan 2019

School

Department

Course

Professor

Math 38 Spring 2011

Midterm Exam 3

Instructions. No calculators, notes, or books are allowed. Please make sure all electronic

devices are turned oﬀ and out of sight. Show all work and cross out work you do not want

graded! Remember to sign your blue book. With your signature you are pledging that you

have neither given nor received assistance on this exam.

Good luck!

1. (10 points): Check following sets of vectors for independence (NO PARTIAL CREDIT):

(a)

1

7

2

,

2

4

−1

,

1

0

−1

,

2

0

−1

(b)

4

3

2

1

,

−2

2

4

8

,

6

8

8

10

2. (15 points): (a) Find the eigenvalues of the matrix A=

1 0 0

−1 2 0

0 1 3

(b) Find eigenvectors for each eigenvalue of the matrix A.

3. (10 points): The matrix A=

1 1 0

1 0 1

1 1 0

has eigenvectors v=

1

1

1

and w=

1

−2

1

.

Find the corresponding eigenvalues.

Page 1 of 2

## Document Summary

Please make sure all electronic devices are turned o and out of sight. Show all work and cross out work you do not want graded! With your signature you are pledging that you have neither given nor received assistance on this exam. Good luck: (10 points): check following sets of vectors for independence (no partial credit): 10: (15 points): (a) find the eigenvalues of the matrix a = 1 3 (b) find eigenvectors for each eigenvalue of the matrix a: (10 points): the matrix a = Page 1 of 2: (10 points): use the row reduction method to solve the following systems: x1 + 2x2 + x3 x4 x5 = 2. 2x1 + 2x2 + 2x3 3x4 2x5 = 1. X3 + 2x4 + x5 = 1. No credit for any other method: (20 points): solve the system of linear di erential equations d~x = a~x, where.