1. Which augmented matrix represents the following system of equations? 1. 2. 3. 4.

2. Which matrix represents the following system of equations? 1. 2. 3.

3. An ice skating rink does not list their prices. I paid £22.25 for 2 children and 3 adults. The group in front of me paid £20.50 for 5 children and 1 adults. Which system of equations would allow us to determine the prices for children and adults 1.2x + 5y = 22.25 3x + y = 20.50 2.2x + 3y = 22.25 5x + y = 20.50 3.22.25x + 20.50y = 42.75 5x + 6y = 11 4.(22.25/2)x + (22.25/3)y = 0 (20.50/5)x + (20.50)y = 0

4. What is the solution to the following system of equations? 2x + 2y = 4 x – y = -6 1.x=½ and y=-¼ 2.x=2 and y=¼ 3.x=-2 and y=4 4.x=2 and y=-4 5.There are an infinite number of solutions 6.There are no solutions

5. What is the solution to the following system of equations? 4x + 2y = 6 -16x - 8y = 12 1.x=3/2 and y=0 2.x=-1/2 and y=4 3.x=0 and y=3 4.x=3 and y=-3 5.There are an infinite number of solutions 6.There are no solutions

6. Which of the following matrices has an inverse? 1. 2. 3. 4.

7. Which of the following matrices does not have an inverse? 1. 2. 3. 4. 5. 6.

8. Let A=. What is the value of A -1 ? 1. 2. 3. 4.

9. Let 1. 2. 3. 4.

10. Calculate. 1. 2. 3. 4.

11. Let A= and B=. What is the value of AB? 1. 2. 3. 4.

12. Let A= and A -1 =. Use this information to solve 3x+y=5 5x+2y=9 What is the value of x? 1.x=2 2.x=0 3.x=1 4.x=-3

13. If A is a 3x4 matrix and B is a 4x2 matrix, then what is the size of AB? 1.3x2 2.4x4 3.2x3 4.None of these

14. The point is transformed by the matrix. Which is its new position? 1. 2. 3. 4.

15. Let and. Calculate. 1. 2. 3.

16. Let A= and B=. Find the element in row 2, column 1 of the product matrix AB.

17. Given two matrices A and B, what must be true about their sizes in order to calculate the matrix product AB? 1.A and B must have the same number of rows 2.A must have as many rows as B has columns 3.A must have as many columns as B has rows

18. If A=,what is A T ? 1. 2. 3. 4.

19. Let A=. Calculate tr(A).

20. Which of the following is an identity matrix? 1. 2. 3. 4.

21. Which of the following is a symmetric matrix? 1. 2. 3. 4.

22. Which of the following relations shows that matrix addition is commutative? 1.A+B=B+A 2.A+(B+C)=(A+B)+C 3.k(A+B)=kA+kB

23. Let and. Calculate. 1. 2. 3.

24. The determinant of a matrix A and the determinant of its transpose A T are not equal. 1.True 2.False 3.Don’t know

25. Calculate the determinant of.

26. The determinant of a 2x2 matrix is -7. What is the determinant of the transpose of this matrix?

27. Which of the following statements is false? 1.If the determinant of a matrix is zero then the matrix has two identical rows. 2.If a square matrix has two identical rows then its determinant is zero. 3.Both are false. 4.Neither are false.

28. Which of the following is an upper triangular matrix? 1. 2. 3. 4.

29. Consider. If then this equation has infinitely many solutions. 1.True 2.False

30. What is the size of this matrix? 1.2 x 3 2.3 x 2 3.6

31. If A and B are both 3x2 matrices then which of the following are not defined? 1.A+B 2.A T B 3.AB 4.AB T 5.All of these are defined

32. Let A= and B=. If A and B are equal what is the value of ?