assignment 1 - math 122

LUTHER COLLEGE AND DEPARTMENT OF MATHEMATICS & STATISTICS

UNIVERSITY OF REGINA

Mathematics 122-L01 – Linear Algebra I

Assignment #1

Quiz #1: Thursday September 18, 2014

In Exercises 1-2, show that the given system has the solution indicated.

1.

2 1

2 2 3 1

Solution:2 3, , 2 2,

2.

3 3 12 3 1

2 0

Solution:2 , 1

3

5

3,

In Exercise 3-4, find the augmented matrix of the given system.

3. 4

2 3 12

4. 2 3 1

3 2 23 5 4 5

In Exercises 5-7, determine which of the given matrices are in reduced row-echelon form.

5. 1 2 00 0

6. 1 1 10 1 00 0 0

7. 1 0 0 20 1 0 10 0 1 2

In Exercises 8-12, solve the linear systems.

8. 5

2 4

9. 2 1

2 53 2 1

10. 2 1

2 02 3 1

11. 2 1

2 02 3 2

12.

2 12 3 1

01

In Exercises 13-14, determine the value(s) of for which the system has no solution, infinitely many solutions or unique solution.

13.

2

2 2

2 2 3 1

2 3

x y z

x y z

x y a z a

14.

2

7 7

2 3 17 16

2 1 3

x y z

x y z

x y a z a

15. Reduce the matrix 2 1 30 2 293 4 5

to row-reduced echelon form without introducing

fractions at any intermediate stage.