# Vectors, Matrices & Determinants: Homeschool Curriculum Chapter Exam

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### Page 1

#### Question 1 1. Solve.

#### Question 2 2. Which of the following is the correct formula for finding the determinant of this matrix?

#### Question 3 3. How many solutions does a dependent system have?

#### Question 4 4. Which of the following would be a square matrix?

#### Question 5 5. Find the determinant of the following matrix.

### Page 2

#### Question 6 6. Which column do you replace in the coefficient matrix if you want to solve for the y solution?

#### Question 7 7. What is the determinant of the minor matrix related to the number 2 in the top row?

#### Question 8 8. Which of the following is not a valid matrix operation?

#### Question 9 9. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

#### Question 10 10. Subtract the following matrices:

### Page 3

#### Question 11 11. 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 12 12. How many solutions does an inconsistent system have?

#### Question 13 13. If you switch the first row with the fourth row, what will the new first row be?

####
Question 14
14.
What is the determinant of the coefficient matrix of this linear system?

2x + 2y = 10

3x - 2y = 0

#### Question 15 15. What is the determinant of the coefficient matrix for this linear system?

### Page 4

#### Question 16 16. How many rows would a matrix that represents a system of 5 variables and 3 equations have?

#### Question 17 17. Which of these statements is not true?

#### Question 18 18. How many solutions does an inconsistent system have?

#### Question 19 19. What is the complete list of equations included in this augmented matrix?

#### Question 20 20. If the determinant of a coefficient matrix equals 0, what does it tell you about the linear system?

### Page 5

#### Question 21 21. What does a vector look like?

#### Question 22 22. Vector A has a magnitude of 7 and vector B has a magnitude of 4. If the angle between them is 20 degrees, what is the dot product?

#### Question 23 23. What is the 'y' length of a vector with a beginning point of (1, -2) and an end point of (-3, 4)

#### Question 24 24. Which row would you multiply by -2 to help you find the inverse matrix?

#### Question 25 25. Which of the following is the inverse of this matrix?

### Page 6

#### Question 26 26. When you multiply matrices, if the first matrix is a 4x3 matrix, which of the following matrices can we multiply with the first?

#### Question 27 27. Which system of equations is represented by the following matrix? (Think of the vertical line as the equal sign.)

#### Question 28 28. What is the x length of a vector with a start point of (1, 2) and an end point of (5, 8)?

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

#### Vectors, Matrices & Determinants: Homeschool Curriculum 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!