# TExES Physics/Math 7-12: Matrices & Determinants Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. Which choice below could be a possible answer to the determinant of a matrix?

#### Question 2 2. Find the determinant of the following matrix.

#### Question 3 3. How many solutions does an inconsistent system have?

#### Question 4 4. Which equation(s) need to be rewritten in this linear system before we can write it in augmented matrix form?

####
Question 5
5.
Solve this linear system.

x + y = 3

y = 1

### Page 2

####
Question 6
6.
In this system of equations, which numbers are your constant numbers?

x + 3y - 2z = 18

2x - y - z = -7

4x - 2y + z = -8

#### Question 7 7. Which of the following is the inverse of this matrix?

#### Question 8 8. Find the determinant.

#### Question 9 9. You are trying to solve a system using Gaussian elimination. In the process, you see that you get 0 for all the rows below the first row. What does this most likely mean for your system?

#### Question 10 10. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

### Page 3

#### Question 11 11. What is the number in the first row and first column in the answer matrix?

#### Question 12 12. What is the first row of our augmented matrix?

#### Question 13 13. Multiply the first row by -3 and add it to the second row.

#### Question 14 14. What is the complete list of equations included in this augmented matrix?

#### Question 15 15. What is the determinant?

### Page 4

#### Question 16 16. Which of the following is the new row that results when you add rows 1 and 3?

#### Question 17 17. Which of the following would be a square matrix?

#### Question 18 18. What is the determinant of the minor matrix related to the number 2 in the top row?

#### Question 19 19. When you multiply matrices, if the first matrix is a 4x3 matrix, which of the following matrices can we multiply with the first?

#### Question 20 20. Rewrite the 3rd equation in proper form so that we can turn it into augmented matrix form.

### Page 5

#### Question 21 21. Which number needs to be changed to find the inverse of this matrix?

#### Question 22 22. Which of the following is NOT true regarding matrices?

#### Question 23 23. For a linear system with two variables, how many determinants do we need to find to find the complete solution using Cramer's rule?

#### Question 24 24. What size is the following matrix?

#### Question 25 25. What form do you need to change your matrix into when using Gauss-Jordan elimination?

### Page 6

#### Question 26 26. Which of these statements is not true?

####
Question 27
27.
Using Gaussian elimination, what number needs to be changed to 0 in this linear system?

3x - 4y = 9

4x + 15y = 11

####
Question 28
28.
Solve this linear system using Gaussian elimination.

x + y = 2

4x - 2y = 0

#### Question 29 29. You are solving a system using Gaussian elimination when you realize that your last row tells you that 0 = 4. You know this to be false, so what does this most likely mean for your system?

#### Question 30 30. Find the determinant.

#### TExES Physics/Math 7-12: Matrices & Determinants Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!