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# Overview of 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. How many solutions does an inconsistent system have?

#### Question 2 2. What matrix do you divide by when using Cramer's Rule?

#### Question 3 3. Which numbers need to be changed to 0 for this linear system?

#### Question 4 4. What is the first row of our augmented matrix?

#### Question 5 5. How many rows would a matrix that represents a system of 5 variables and 3 equations have?

### Page 2

#### Question 6 6. Add the following matrices:

#### Question 7 7. What is the determinant of the coefficient matrix for this linear system?

####
Question 8
8.
In this system of equations, which numbers are your constant numbers?

x + 3y - 2z = 18

2x - y - z = -7

4x - 2y + z = -8

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

### Page 3

#### Question 11 11. The identity matrix can be likened to what number?

#### Question 12 12. Which row would you multiply by -2 to help you find the inverse matrix?

#### Question 13 13. What size is the following matrix?

#### Question 14 14. Which choice below could be a possible answer to the determinant of a matrix?

#### Question 15 15. If you switch the first row with the fourth row, what will the new first row be?

### Page 4

#### Question 16 16. Multiply the first row by -3 and add it to the second row.

#### Question 17 17. Which of the following is the inverse of this matrix?

#### Question 18 18. Which of these statements is not true?

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

### Page 5

#### Question 21 21. What is the complete list of equations included in this augmented matrix?

#### Question 22 22. Which equation(s) need to be rewritten in this linear system before we can write it in augmented matrix form?

#### Question 23 23. Find the determinant.

#### Question 24 24. Which of the following is the correct formula for finding the determinant of this matrix?

#### Question 25 25. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

### Page 6

####
Question 26
26.
Find the y solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

####
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. How many equations are needed in a linear system with five variables?

#### Question 29 29. How many solutions does a dependent system have?

#### Question 30 30. Which of the following is NOT a correct description of the reduced row echelon form?

#### Overview of 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!