Math · Drill 33

Math practice 33

88 questions ~15 min recommended

⏱ 00:00

Score

—

1. Matrices $A$ and $B$ represent two coded messages combined by addition. What is $A+B$ if $$A=\begin{bmatrix}-1 & 3\\ 4 & -2\end{bmatrix},\quad B=\begin{bmatrix}5 & -3\\ -2 & 1\end{bmatrix}?$$

A. $$$\begin{bmatrix}-6 & 6\\ -8 & 3\end{bmatrix}$$

B. $$$\begin{bmatrix}4 & 0\\ 2 & -1\end{bmatrix}$$

C. $$$\begin{bmatrix}-5 & 0\\ -8 & -3\end{bmatrix}$$

D. $$$\begin{bmatrix}4 & 6\\ 2 & -1\end{bmatrix}$$

2. Which of the following matrices is equal to $3 \begin{bmatrix} 2 & -1 \\ 4 & 0 \end{bmatrix}$?

A. $$\begin{bmatrix} 5 & 2 \\ 7 & 3 \end{bmatrix}$

B. $$\begin{bmatrix} 5 & -3 \\ 7 & 0 \end{bmatrix}$

C. $$\begin{bmatrix} 6 & -1 \\ 12 & 0 \end{bmatrix}$

D. $$\begin{bmatrix} 6 & -3 \\ 12 & 0 \end{bmatrix}$

3. If $A = \begin{pmatrix} 3 & -2 \\ 1 & 4 \end{pmatrix}$, what is $-A$?

A. $$\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix}$

B. $$\begin{pmatrix} -3 & -2 \\ 1 & -4 \end{pmatrix}$

C. $$\begin{pmatrix} 3 & -2 \\ -1 & 4 \end{pmatrix}$

D. $$\begin{pmatrix} -3 & 2 \\ -1 & -4 \end{pmatrix}$

4. If $A = \begin{pmatrix} 0 & 1 \\ -2 & 4 \end{pmatrix}$, what is $-3A$?

A. $$\begin{pmatrix} 0 & -3 \\ -6 & 12 \end{pmatrix}$

B. $$\begin{pmatrix} 0 & 3 \\ -6 & 12 \end{pmatrix}$

C. $$\begin{pmatrix} 0 & 1 \\ -2 & 4 \end{pmatrix}$

D. $$\begin{pmatrix} 0 & -3 \\ 6 & -12 \end{pmatrix}$

5. Which of the following is the product $AB$ for matrices $A = \begin{pmatrix} 0 & 1 \\ 2 & -1 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 2 \\ 1 & 0 \end{pmatrix}$?

A. $$\begin{pmatrix} 3 & 0 \\ 6 & 4 \end{pmatrix}$

B. $$\begin{pmatrix} 1 & 2 \\ 5 & 4 \end{pmatrix}$

C. $$\begin{pmatrix} 1 & 0 \\ 5 & 4 \end{pmatrix}$

D. $$\begin{pmatrix} 1 & 0 \\ 5 & 2 \end{pmatrix}$

6. If $A = \begin{pmatrix} 3 & -2 \\ 0 & 1 \end{pmatrix}$, what is $3A$?

A. $$\begin{pmatrix} 9 & -6 \\ 0 & 3 \end{pmatrix}$

B. $$\begin{pmatrix} 3 & -6 \\ 0 & 3 \end{pmatrix}$

C. $$\begin{pmatrix} 6 & -4 \\ 0 & 2 \end{pmatrix}$

D. $$\begin{pmatrix} 9 & -2 \\ 0 & 1 \end{pmatrix}$

7. What is the determinant of matrix $\begin{pmatrix} 2 & -1 \\ 3 & 4 \end{pmatrix}$?

A. -11

B. -10

C. 10

D. 11

8. What is the determinant of matrix $\begin{pmatrix} 3 & 1 \\ 2 & 2 \end{pmatrix}$?

A. 3

B. 4

C. 5

D. 6

9. What is the determinant of matrix $\begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix}$?

A. 4

B. 8

C. 10

D. 14

10. What is the determinant of the matrix $$\begin{bmatrix}-3 & 2\\ 4 & 1\end{bmatrix}?$$

A. $$-5$

B. $$-11$

C. $$11$

D. $$5$

11. What is $A + B$ for matrices $A$ and $B$ given by $$A=\begin{bmatrix}2 & -1\\ 0 & 3\end{bmatrix},\quad B=\begin{bmatrix}-4 & 5\\ 1 & -2\end{bmatrix}?$$

A. $$$\begin{bmatrix}6 & -6\\ -1 & 5\end{bmatrix}$$

B. $$$\begin{bmatrix}-2 & 4\\ 1 & 1\end{bmatrix}$$

C. $$$\begin{bmatrix}-2 & -6\\ -1 & 5\end{bmatrix}$$

D. $$$\begin{bmatrix}-8 & 5\\ 0 & -6\end{bmatrix}$$

12. A transformation scales every coordinate by $-3$. If $$A=\begin{bmatrix}-1 & 2\\ 0 & 4\end{bmatrix},$$ what is $-3A$?

A. $$$\begin{bmatrix}3 & -1\\ 0 & -12\end{bmatrix}$$

B. $$$\begin{bmatrix}3 & -6\\ 0 & -12\end{bmatrix}$$

C. $$$\begin{bmatrix}1 & -2\\ 0 & -4\end{bmatrix}$$

D. $$$\begin{bmatrix}-3 & 6\\ 0 & 12\end{bmatrix}$$

13. A matrix $A$ is used to encode a 2-variable system. If $$A=\begin{bmatrix}0 & -3\\ 2 & 1\end{bmatrix},$$ what is $-2A$?

A. $$$\begin{bmatrix}0 & -1\\ -4 & -2\end{bmatrix}$$

B. $$$\begin{bmatrix}0 & -6\\ -4 & -2\end{bmatrix}$$

C. $$$\begin{bmatrix}0 & 6\\ -4 & -2\end{bmatrix}$$

D. $$$\begin{bmatrix}0 & 6\\ 4 & 2\end{bmatrix}$$

14. What is A - B for matrices $A = \begin{bmatrix} 0 & 4 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 1 \\ 3 & 0 \end{bmatrix}$?

A. $$\begin{bmatrix} 2 & 3 \\ -6 & 0 \end{bmatrix}$

B. $$\begin{bmatrix} 0 & 5 \\ 0 & 2 \end{bmatrix}$

C. $$\begin{bmatrix} 0 & 4 \\ 0 & 2 \end{bmatrix}$

D. $$\begin{bmatrix} 2 & 3 \\ -6 & 2 \end{bmatrix}$

15. If $A = \begin{bmatrix} 0 & 1 \\ 4 & -3 \end{bmatrix}$, what is $-1A$?

A. $$\begin{bmatrix} 0 & 1 \\ -4 & 3 \end{bmatrix}$

B. $$\begin{bmatrix} 0 & -1 \\ -4 & 3 \end{bmatrix}$

C. $$\begin{bmatrix} 0 & 1 \\ 4 & -3 \end{bmatrix}$

D. $$\begin{bmatrix} 0 & -1 \\ 4 & -3 \end{bmatrix}$

16. Two sensors produce readings stored in matrices. What is $A+B$ if $A=\begin{bmatrix}0 & 3\\ -5 & 2\end{bmatrix}$ and $B=\begin{bmatrix}1 & -4\\ 2 & 1\end{bmatrix}$?

A. $$\begin{bmatrix}1 & 7\\ -3 & 3\end{bmatrix}$

B. $$\begin{bmatrix}-1 & 7\\ -7 & 1\end{bmatrix}$

C. $$\begin{bmatrix}0 & -12\\ -10 & 2\end{bmatrix}$

D. $$\begin{bmatrix}1 & -1\\ -3 & 3\end{bmatrix}$

17. Which of the following is the product $AB$ for matrices $A = \begin{pmatrix} 0 & 2 \\ 1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$?

A. $$\begin{pmatrix} 6 & 2 \\ 6 & 3 \end{pmatrix}$

B. $$\begin{pmatrix} 4 & 2 \\ 7 & 3 \end{pmatrix}$

C. $$\begin{pmatrix} 4 & 3 \\ 6 & 3 \end{pmatrix}$

D. $$\begin{pmatrix} 4 & 2 \\ 7 & 4 \end{pmatrix}$

18. What is A + B for matrices $A = \begin{pmatrix} 2 & 0 \\ -1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ 2 & -2 \end{pmatrix}$?

A. $$\begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}$

B. $$\begin{pmatrix} 2 & 0 \\ 1 & -5 \end{pmatrix}$

C. $$\begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix}$

D. $$\begin{pmatrix} 2 & 1 \\ -1 & 3 \end{pmatrix}$

19. What is the determinant of matrix $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$?

A. -10

B. -2

C. 2

D. 10

20. Let $$A=\begin{bmatrix}1 & 2\\ -1 & 3\end{bmatrix}$$ and $$B=\begin{bmatrix}0 & -2\\ 4 & 1\end{bmatrix}.$$ Which of the following is the product $AB$?

A. $$$\begin{bmatrix}8 & 12\\ 0 & 5\end{bmatrix}$$

B. $$$\begin{bmatrix}8 & 0\\ 12 & -1\end{bmatrix}$$

C. $$$\begin{bmatrix}8 & 0\\ 12 & 5\end{bmatrix}$$

D. $$$\begin{bmatrix}0 & -4\\ -4 & 3\end{bmatrix}$$

21. Two matrices represent consecutive transformations on a vector. Which of the following is the product $AB$ if $$A=\begin{bmatrix}0 & 2\\ -1 & 3\end{bmatrix},\quad B=\begin{bmatrix}5 & -2\\ 1 & 4\end{bmatrix}?$

A. $$$\begin{bmatrix}0 & -4\\ -1 & 12\end{bmatrix}$$

B. $$$\begin{bmatrix}2 & 8\\ -2 & 14\end{bmatrix}$$

C. $$$\begin{bmatrix}2 & -4\\ -5 & 12\end{bmatrix}$$

D. $$$\begin{bmatrix}2 & 8\\ -8 & 14\end{bmatrix}$$

22. Let $$A=\begin{bmatrix}4 & -1\\ 2 & 5\end{bmatrix}$$ and $$B=\begin{bmatrix}1 & 3\\ -2 & 0\end{bmatrix}.$$ What is $A-B$?

A. $$$\begin{bmatrix}3 & -4\\ 4 & 5\end{bmatrix}$$

B. $$$\begin{bmatrix}3 & 2\\ 4 & 5\end{bmatrix}$$

C. $$$\begin{bmatrix}5 & 2\\ 0 & 5\end{bmatrix}$$

D. $$$\begin{bmatrix}3 & -4\\ 0 & 5\end{bmatrix}$$

23. What is A + B for matrices $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix}$?

A. $$\begin{bmatrix} 5 & 5 \\ 5 & 5 \end{bmatrix}$

B. $$\begin{bmatrix} 4 & 2 \\ 2 & 4 \end{bmatrix}$

C. $$\begin{bmatrix} 3 & 5 \\ 5 & 3 \end{bmatrix}$

D. $$\begin{bmatrix} 5 & 3 \\ 3 & 5 \end{bmatrix}$

24. If $A = \begin{bmatrix} 3 & 5 \\ -2 & 4 \end{bmatrix}$, what is $-2A$?

A. $$\begin{bmatrix} 6 & 10 \\ -4 & 8 \end{bmatrix}$

B. $$\begin{bmatrix} -6 & -10 \\ 4 & -8 \end{bmatrix}$

C. $$\begin{bmatrix} 6 & -10 \\ -4 & -8 \end{bmatrix}$

D. $$\begin{bmatrix} -6 & 10 \\ 4 & 8 \end{bmatrix}$

25. What is the determinant of matrix $\begin{bmatrix} 2 & -3 \\ 4 & 1 \end{bmatrix}$?

A. -10

B. 6

C. 10

D. 14

26. What is the determinant of matrix $\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$?

A. 2

B. 10

C. 11

D. 14

27. If $A = \begin{bmatrix} -1 & 2 \\ 3 & -4 \end{bmatrix}$, what is $2A$?

A. $$\begin{bmatrix} -2 & 4 \\ 6 & -8 \end{bmatrix}$

B. $$\begin{bmatrix} -1 & 4 \\ 3 & -8 \end{bmatrix}$

C. $$\begin{bmatrix} -1 & 2 \\ 6 & -4 \end{bmatrix}$

D. $$\begin{bmatrix} -2 & 2 \\ 3 & -4 \end{bmatrix}$

28. Which of the following is the product $AB$ if $A = \begin{bmatrix} 2 & 3 \\ 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}$?

A. $$\begin{bmatrix} 2 & 5 \\ -1 & 4 \end{bmatrix}$

B. $$\begin{bmatrix} 2 & 5 \\ 1 & -4 \end{bmatrix}$

C. $$\begin{bmatrix} 2 & 5 \\ 1 & 0 \end{bmatrix}$

D. $$\begin{bmatrix} 2 & 5 \\ 1 & 4 \end{bmatrix}$

29. What is A - B for matrices $A = \begin{bmatrix} 3 & -2 \\ 1 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 1 \\ -1 & 2 \end{bmatrix}$?

A. $$\begin{bmatrix} 4 & -1 \\ 2 & 7 \end{bmatrix}$

B. $$\begin{bmatrix} 2 & -2 \\ 0 & 3 \end{bmatrix}$

C. $$\begin{bmatrix} 2 & -3 \\ 2 & 3 \end{bmatrix}$

D. $$\begin{bmatrix} 3 & -1 \\ 2 & 3 \end{bmatrix}$

30. Which of the following is the product $AB$ if $A = \begin{bmatrix} 1 & 0 \\ -2 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 1 \\ 0 & 4 \end{bmatrix}$?

A. $$\begin{bmatrix} 2 & 4 \\ -4 & 8 \end{bmatrix}$

B. $$\begin{bmatrix} 2 & 1 \\ -4 & 10 \end{bmatrix}$

C. $$\begin{bmatrix} 2 & 4 \\ -4 & 12 \end{bmatrix}$

D. $$\begin{bmatrix} 1 & 0 \\ -2 & 12 \end{bmatrix}$

31. What is the determinant of matrix $\begin{bmatrix} -4 & 2 \\ 1 & -3 \end{bmatrix}$?

A. -10

B. 10

C. 12

D. 14

32. Which of the following is the product $AB$ if $A = \begin{bmatrix} 0 & 2 \\ 3 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 4 & 0 \end{bmatrix}$?

A. $$\begin{bmatrix} 8 & 0 \\ 7 & 3 \end{bmatrix}$

B. $$\begin{bmatrix} 8 & 0 \\ 7 & -3 \end{bmatrix}$

C. $$\begin{bmatrix} 8 & 0 \\ 3 & 4 \end{bmatrix}$

D. $$\begin{bmatrix} 8 & 0 \\ 3 & 12 \end{bmatrix}$

33. What is A + B for matrices $A = \begin{bmatrix} -3 & 0 \\ 4 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & -1 \\ 2 & 2 \end{bmatrix}$?

A. $$\begin{bmatrix} 0 & -1 \\ 6 & 1 \end{bmatrix}$

B. $$\begin{bmatrix} 0 & 1 \\ 2 & 3 \end{bmatrix}$

C. $$\begin{bmatrix} 0 & -1 \\ 6 & 3 \end{bmatrix}$

D. $$\begin{bmatrix} 0 & 1 \\ 4 & 1 \end{bmatrix}$

34. If $A = \begin{bmatrix} 2 & -3 \\ 5 & 1 \end{bmatrix}$, what is $3A$?

A. $$\begin{bmatrix} 6 & 9 \\ 15 & 3 \end{bmatrix}$

B. $$\begin{bmatrix} 6 & -9 \\ 15 & 3 \end{bmatrix}$

C. $$\begin{bmatrix} 6 & -3 \\ 5 & 3 \end{bmatrix}$

D. $$\begin{bmatrix} 2 & -3 \\ 15 & 3 \end{bmatrix}$

35. Two teams track their weekly performance using matrices. What is $A+B$ for matrices $A=\begin{bmatrix}2 & -1\\ 3 & 0\end{bmatrix}$ and $B=\begin{bmatrix}-4 & 5\\ 1 & -2\end{bmatrix}$?

A. $$\begin{bmatrix}-2 & 4\\ 4 & -2\end{bmatrix}$

B. $$\begin{bmatrix}-2 & 6\\ 2 & -2\end{bmatrix}$

C. $$\begin{bmatrix}-8 & -5\\ 3 & 0\end{bmatrix}$

D. $$\begin{bmatrix}6 & -6\\ 4 & 2\end{bmatrix}$

36. Two 2×2 matrices summarize results from two trials. What is $A+B$ if $A=\begin{bmatrix}-3 & 2\\ 5 & -1\end{bmatrix}$ and $B=\begin{bmatrix}4 & -2\\ -1 & 3\end{bmatrix}$?

A. $$\begin{bmatrix}1 & 4\\ 4 & 2\end{bmatrix}$

B. $$\begin{bmatrix}1 & 0\\ 4 & 2\end{bmatrix}$

C. $$\begin{bmatrix}-12 & -4\\ -5 & -3\end{bmatrix}$

D. $$\begin{bmatrix}-7 & 4\\ 6 & -4\end{bmatrix}$

37. A data table is doubled to reflect two weeks instead of one. If $A=\begin{bmatrix}5 & -1\\ -3 & 2\end{bmatrix}$, what is $2A$?

A. $$\begin{bmatrix}10 & -2\\ -6 & 4\end{bmatrix}$

B. $$\begin{bmatrix}7 & 1\\ -1 & 4\end{bmatrix}$

C. $$\begin{bmatrix}25 & -2\\ 9 & 4\end{bmatrix}$

D. $$\begin{bmatrix}10 & 2\\ 6 & 4\end{bmatrix}$

38. A matrix of coefficients is scaled to change units. What is $4A$ if $A=\begin{bmatrix}-1 & 0\\ 2 & -3\end{bmatrix}$?

A. $$\begin{bmatrix}-4 & 0\\ 6 & -9\end{bmatrix}$

B. $$\begin{bmatrix}3 & 4\\ 6 & 1\end{bmatrix}$

C. $$\begin{bmatrix}4 & 0\\ -8 & 12\end{bmatrix}$

D. $$\begin{bmatrix}-4 & 0\\ 8 & -12\end{bmatrix}$

39. A 2×2 matrix is used to represent a linear map. What is the determinant of $\begin{bmatrix}-4 & 1\\ 2 & 3\end{bmatrix}$?

A. $$-10$

B. $$14$

C. $$-14$

D. $$10$

40. A 2D transformation is represented by the matrix $\begin{bmatrix}a & b\\ c & d\end{bmatrix}$. What is the determinant of $\begin{bmatrix}3 & -2\\ 5 & 1\end{bmatrix}$?

A. $$-7$

B. $$-13$

C. $$7$

D. $$13$

41. A matrix is scaled to represent three identical copies of a system. If $A=\begin{bmatrix}1 & -3\\ 4 & 0\end{bmatrix}$, what is $3A$?

A. $$\begin{bmatrix}1 & -9\\ 4 & 0\end{bmatrix}$

B. $$\begin{bmatrix}3 & -6\\ 7 & 0\end{bmatrix}$

C. $$\begin{bmatrix}3 & -9\\ 12 & 0\end{bmatrix}$

D. $$\begin{bmatrix}-3 & 9\\ -12 & 0\end{bmatrix}$

42. A matrix of values is scaled down by a factor of 2. What is $\left(-\tfrac{1}{2}\right)A$ if $A=\begin{bmatrix}4 & -2\\ -6 & 0\end{bmatrix}$?

A. $$\begin{bmatrix}-2 & 1\\ 3 & 0\end{bmatrix}$

B. $$\begin{bmatrix}-8 & 4\\ 12 & 0\end{bmatrix}$

C. $$\begin{bmatrix}2 & -1\\ -3 & 0\end{bmatrix}$

D. $$\begin{bmatrix}-2 & -1\\ 3 & 0\end{bmatrix}$

43. A graphics filter scales every entry of a matrix by a constant. What is $-3A$ if $A=\begin{bmatrix}-1 & 2\\ 0 & 4\end{bmatrix}$?

A. $$\begin{bmatrix}3 & -6\\ 0 & -12\end{bmatrix}$

B. $$\begin{bmatrix}-3 & -6\\ 0 & -12\end{bmatrix}$

C. $$\begin{bmatrix}-3 & 6\\ 0 & 12\end{bmatrix}$

D. $$\begin{bmatrix}3 & -2\\ 0 & -4\end{bmatrix}$

44. A system updates a state vector by multiplying matrices. Which of the following is the product $AB$ if $A=\begin{bmatrix}2 & -1\\ 0 & 3\end{bmatrix}$ and $B=\begin{bmatrix}-2 & 4\\ 1 & -1\end{bmatrix}$?

A. $$\begin{bmatrix}-5 & 9\\ 3 & -3\end{bmatrix}$

B. $$\begin{bmatrix}-5 & 8\\ 3 & -3\end{bmatrix}$

C. $$\begin{bmatrix}-3 & 9\\ 3 & -3\end{bmatrix}$

D. $$\begin{bmatrix}-4 & -4\\ 0 & -3\end{bmatrix}$

45. A class compares two 2×2 data matrices by subtracting them. What is $A-B$ if $A=\begin{bmatrix}4 & -2\\ 0 & 1\end{bmatrix}$ and $B=\begin{bmatrix}-1 & 3\\ 2 & -4\end{bmatrix}$?

A. $$\begin{bmatrix}5 & -5\\ -2 & 5\end{bmatrix}$

B. $$\begin{bmatrix}5 & 1\\ 2 & -3\end{bmatrix}$

C. $$\begin{bmatrix}3 & 1\\ 2 & -3\end{bmatrix}$

D. $$\begin{bmatrix}-5 & 5\\ 2 & -5\end{bmatrix}$

46. For a 2×2 matrix $\begin{bmatrix}a & b\\ c & d\end{bmatrix}$, the determinant is $ad-bc$. What is the determinant of $\begin{bmatrix}2 & 5\\ -1 & 4\end{bmatrix}$?

A. $$-13$

B. $$13$

C. $$3$

D. $$-3$

47. A student records changes in two quantities using matrices. What is $A-B$ if $A=\begin{bmatrix}-2 & 4\\ 1 & -3\end{bmatrix}$ and $B=\begin{bmatrix}3 & -1\\ -2 & 5\end{bmatrix}$?

A. $$\begin{bmatrix}-5 & 5\\ 3 & -8\end{bmatrix}$

B. $$\begin{bmatrix}1 & 3\\ -1 & 2\end{bmatrix}$

C. $$\begin{bmatrix}-5 & 3\\ -1 & 2\end{bmatrix}$

D. $$\begin{bmatrix}5 & -5\\ -3 & 8\end{bmatrix}$

48. A student combines two data matrices by subtraction: $A=[4,0,-2,1]$ and $B=[1,-3,5,2]$. What is $A-B$?

A. $$[[3,3],[3,3]]$

B. $$[[3,3],[-7,-1]]$

C. $$[[5,-3],[3,3]]$

D. $$[[3,-3],[7,1]]$

49. A shipping clerk records two $2\times2$ matrices of daily package counts, $A=[2,-1,3,4]$ and $B=[-3,5,1,-2]$. What is $A+B$?

A. $$[[ -5, 4 ],[ 4, 2 ]]$

B. $$[[ -1, 4 ],[ 4, 2 ]]$

C. $$[[ -1, 6 ],[ 2, 6 ]]$

D. $$[[ 1, -6 ],[ 3, -8 ]]$

50. A graphics routine multiplies matrices $A=[2,1,3,-2]$ and $B=[1,-3,4,0]$. Which of the following is the product $AB$?

A. $$[[6,-6],[-5,-9]]$

B. $$[[2,-3],[12,0]]$

C. $$[[6,-6],[5,9]]$

D. $$[[6,-5],[-6,-9]]$

51. If $A=[3,-2,0,5]$ represents a simple linear transformation, what is $2A$?

A. $$[[1,-1],[0,2]]$

B. $$[[6,-4],[0,10]]$

C. $$[[5,0],[2,7]]$

D. $$[[6,4],[0,10]]$

52. Let $$A=\begin{bmatrix}2 & -1\\ 3 & 0\end{bmatrix}$$ and $$B=\begin{bmatrix}-4 & 5\\ 1 & -2\end{bmatrix}.$$ What is $A+B$ for matrices $A$ and $B$?

A. $$$\begin{bmatrix}-8 & 4\\ 3 & 0\end{bmatrix}$$

B. $$$\begin{bmatrix}2 & -5\\ 3 & 0\end{bmatrix}$$

C. $$$\begin{bmatrix}-2 & 4\\ 4 & -2\end{bmatrix}$$

D. $$$\begin{bmatrix}-2 & 6\\ 2 & -2\end{bmatrix}$$

53. A robotics team scales a transformation matrix $A=[ -2, 3 , 1, 0 ]$ by a factor of $k=-3$. What is $kA$?

A. $$[[ 6, 9 ],[ -3, 0 ]]$

B. $$[[ 6, -9 ],[ -3, 0 ]]$

C. $$[[ -6, -9 ],[ 3, 0 ]]$

D. $$[[ -6, 9 ],[ 3, 0 ]]$

54. A control system applies matrix $A=[ -1, 4 , 2, 1 ]$ and then $B=[ 3, 0 , -2, 5 ]$. Which of the following is the product $AB$?

A. $$[[ -3, 0 ],[ -4, 5 ]]$

B. $$[[ 11, 20 ],[ -4, 5 ]]$

C. $$[[ -11, 4 ],[ 20, 5 ]]$

D. $$[[ -11, 20 ],[ 4, 5 ]]$

55. Let $$A=\begin{bmatrix}2 & -1\\ 3 & 0\end{bmatrix}$$ and $$B=\begin{bmatrix}-4 & 5\\ 1 & -2\end{bmatrix}.$$ What is $A+B$ for matrices $A$ and $B$?

A. $$$\begin{bmatrix}-8 & 4\\ 3 & 0\end{bmatrix}$$

B. $$$\begin{bmatrix}-2 & 4\\ 4 & -2\end{bmatrix}$$

C. $$$\begin{bmatrix}-2 & 6\\ 2 & -2\end{bmatrix}$$

D. $$$\begin{bmatrix}2 & -5\\ 3 & 0\end{bmatrix}$$

56. What is the determinant of the matrix $$\begin{bmatrix}2 & -5\\ 1 & 3\end{bmatrix}?$$

A. $$11$

B. $$-11$

C. $$1$

D. $$-1$

57. Let $$A=\begin{bmatrix}-2 & 1\\ 3 & -1\end{bmatrix}$$ and $$B=\begin{bmatrix}5 & 0\\ -4 & 2\end{bmatrix}.$$ Which of the following is the product $AB$?

A. $$$\begin{bmatrix}-14 & 2\\ 19 & -2\end{bmatrix}$$

B. $$$\begin{bmatrix}-14 & 19\\ 2 & -2\end{bmatrix}$$

C. $$$\begin{bmatrix}-10 & 0\\ -12 & -2\end{bmatrix}$$

D. $$$\begin{bmatrix}-14 & 2\\ 11 & -2\end{bmatrix}$$

58. A matrix $A$ is scaled by $-3$ to reverse direction and triple magnitude. What is $-3A$ if $$A=\begin{bmatrix}1 & -4\\ -2 & 3\end{bmatrix}?$$

A. $$$\begin{bmatrix}-3 & -12\\ -6 & -9\end{bmatrix}$$

B. $$$\begin{bmatrix}-3 & 12\\ 6 & -9\end{bmatrix}$$

C. $$$\begin{bmatrix}3 & -12\\ -6 & 9\end{bmatrix}$$

D. $$$\begin{bmatrix}-2 & 1\\ 4 & -3\end{bmatrix}$$

59. Which of the following is the product $AB$ if $$A=\begin{bmatrix}2 & 1\\ -3 & 4\end{bmatrix},\quad B=\begin{bmatrix}-1 & 0\\ 5 & 2\end{bmatrix}?$$

A. $$$\begin{bmatrix}3 & 0\\ 23 & 8\end{bmatrix}$$

B. $$$\begin{bmatrix}-2 & 0\\ -15 & 8\end{bmatrix}$$

C. $$$\begin{bmatrix}3 & 2\\ -7 & 8\end{bmatrix}$$

D. $$$\begin{bmatrix}3 & 2\\ 23 & 8\end{bmatrix}$$

60. Two matrices represent changes in inventory at two warehouses. What is $A+B$ for matrices $A$ and $B$ if $$A=\begin{bmatrix}2 & -1\\ 0 & 3\end{bmatrix},\quad B=\begin{bmatrix}-4 & 5\\ 1 & -2\end{bmatrix}?$$

A. $$$\begin{bmatrix}-2 & 4\\ 1 & 1\end{bmatrix}$$

B. $$$\begin{bmatrix}-2 & 6\\ 1 & 1\end{bmatrix}$$

C. $$$\begin{bmatrix}-8 & -5\\ 0 & -6\end{bmatrix}$$

D. $$$\begin{bmatrix}6 & -6\\ -1 & 5\end{bmatrix}$$

61. Matrices $A$ and $B$ track net gains and losses over two days. What is $A-B$ if $$A=\begin{bmatrix}0 & 4\\ -2 & 1\end{bmatrix},\quad B=\begin{bmatrix}3 & -1\\ 5 & 2\end{bmatrix}?$$

A. $$$\begin{bmatrix}-3 & 5\\ -7 & -1\end{bmatrix}$$

B. $$$\begin{bmatrix}-3 & 3\\ 7 & -1\end{bmatrix}$$

C. $$$\begin{bmatrix}3 & -5\\ 7 & 1\end{bmatrix}$$

D. $$$\begin{bmatrix}3 & 3\\ 3 & 3\end{bmatrix}$$

62. Two $2\times 2$ matrices model a two-step process. Which of the following is the product $AB$ if $$A=\begin{bmatrix}1 & -2\\ 3 & 0\end{bmatrix},\quad B=\begin{bmatrix}4 & 1\\ -1 & 2\end{bmatrix}?$$

A. $$$\begin{bmatrix}6 & -3\\ 12 & 3\end{bmatrix}$$

B. $$$\begin{bmatrix}6 & -3\\ 3 & 0\end{bmatrix}$$

C. $$$\begin{bmatrix}2 & -3\\ 12 & 3\end{bmatrix}$$

D. $$$\begin{bmatrix}4 & -2\\ -3 & 0\end{bmatrix}$$

63. What is the determinant of $$\begin{bmatrix}-4 & 1 \\ 2 & -3\end{bmatrix}$$?

A. $$10$

B. $$-10$

C. $$-14$

D. $$14$

64. A transformation matrix $A$ is scaled to double its effect. If $$A=\begin{bmatrix}-3 & 2\\ 5 & 0\end{bmatrix},$$ what is $2A$?

A. $$$\begin{bmatrix}-6 & 4\\ 10 & 0\end{bmatrix}$$

B. $$$\begin{bmatrix}-9 & 6\\ 15 & 0\end{bmatrix}$$

C. $$$\begin{bmatrix}-6 & 4\\ 5 & 0\end{bmatrix}$$

D. $$$\begin{bmatrix}-1 & 4\\ 10 & 2\end{bmatrix}$$

65. If $A = \begin{bmatrix} 3 & -2 \\ 1 & 0 \end{bmatrix}$, which of the following matrices is equal to $4A$

A. $$\begin{bmatrix} 12 & -2 \\ 1 & 0 \end{bmatrix}$

B. $$\begin{bmatrix} 7 & 2 \\ 5 & 4 \end{bmatrix}$

C. $$\begin{bmatrix} -1 & 6 \\ -3 & 0 \end{bmatrix}$

D. $$\begin{bmatrix} 12 & -8 \\ 4 & 0 \end{bmatrix}$

66. What is A + B for matrices $A = \begin{pmatrix} 1 & -2 \\ 0 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 1 \\ -1 & 2 \end{pmatrix}$?

A. $$\begin{pmatrix} 2 & -1 \\ -1 & 1 \end{pmatrix}$

B. $$\begin{pmatrix} 4 & 3 \\ 1 & 5 \end{pmatrix}$

C. $$\begin{pmatrix} 4 & 1 \\ 0 & 5 \end{pmatrix}$

D. $$\begin{pmatrix} 4 & -1 \\ -1 & 5 \end{pmatrix}$

67. What is the determinant of matrix $\begin{pmatrix} 1 & 1 \\ 2 & 2 \end{pmatrix}$?

A. -1

B. 0

C. 1

D. 2

68. What is A + B for matrices $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 3 \\ 2 & 1 \end{pmatrix}$?

A. $$\begin{pmatrix} 5 & 5 \\ 5 & 5 \end{pmatrix}$

B. $$\begin{pmatrix} 3 & 5 \\ 5 & 3 \end{pmatrix}$

C. $$\begin{pmatrix} -3 & -1 \\ 1 & 3 \end{pmatrix}$

D. $$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$

69. What is the determinant of matrix $\begin{pmatrix} 5 & 2 \\ 1 & -3 \end{pmatrix}$?

A. -17

B. -13

C. 13

D. 17

70. What is the determinant of matrix $\begin{pmatrix} 2 & 1 \\ 5 & 3 \end{pmatrix}$?

A. -1

B. 1

C. 3

D. 5

71. If $A = \begin{pmatrix} 5 & 0 \\ -2 & 3 \end{pmatrix}$, what is $-A$?

A. $$\begin{pmatrix} -5 & 0 \\ 2 & -3 \end{pmatrix}$

B. $$\begin{pmatrix} 5 & 0 \\ 2 & -3 \end{pmatrix}$

C. $$\begin{pmatrix} -5 & 0 \\ -2 & 3 \end{pmatrix}$

D. $$\begin{pmatrix} 5 & 0 \\ -2 & 3 \end{pmatrix}$

72. What is A + B for matrices $A = \begin{pmatrix} -3 & 2 \\ 1 & 0 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & -1 \\ 2 & 3 \end{pmatrix}$?

A. $$\begin{pmatrix} -7 & 3 \\ -3 & -3 \end{pmatrix}$

B. $$\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}$

C. $$\begin{pmatrix} 1 & 1 \\ 3 & 3 \end{pmatrix}$

D. $$\begin{pmatrix} 7 & -3 \\ 3 & 3 \end{pmatrix}$

73. What is the determinant of matrix $\begin{pmatrix} 3 & 0 \\ 2 & 5 \end{pmatrix}$?

A. -6

B. 5

C. 6

D. 15

74. If $A = \begin{pmatrix} 0 & 2 \\ -3 & 1 \end{pmatrix}$, what is $2A$?

A. $$\begin{pmatrix} 0 & 2 \\ -3 & 1 \end{pmatrix}$

B. $$\begin{pmatrix} 0 & 2 \\ -6 & 1 \end{pmatrix}$

C. $$\begin{pmatrix} 0 & 4 \\ -6 & 2 \end{pmatrix}$

D. $$\begin{pmatrix} 0 & 4 \\ -3 & 2 \end{pmatrix}$

75. What is $A - B$ for matrices $A$ and $B$ given by $$A=\begin{bmatrix}-3 & 1\\ 2 & -5\end{bmatrix},\quad B=\begin{bmatrix}2 & -4\\ -1 & 3\end{bmatrix}?$$

A. $$$\begin{bmatrix}-1 & -3\\ 1 & -2\end{bmatrix}$$

B. $$$\begin{bmatrix}-5 & 5\\ 3 & -8\end{bmatrix}$$

C. $$$\begin{bmatrix}5 & -5\\ -3 & 8\end{bmatrix}$$

D. $$$\begin{bmatrix}-5 & -3\\ 1 & -2\end{bmatrix}$$

76. What is the determinant of the matrix $$\begin{bmatrix}2 & 5\\ -1 & 3\end{bmatrix}?$$

A. $$-11$

B. $$11$

C. $$-1$

D. $$1$

77. A matrix $A$ records net changes in two accounts. If $$A=\begin{bmatrix}-2 & 1\\ 5 & -3\end{bmatrix},$$ what is $2A$?

A. $$$\begin{bmatrix}-4 & 2\\ 10 & 6\end{bmatrix}$$

B. $$$\begin{bmatrix}-4 & 2\\ 10 & -6\end{bmatrix}$$

C. $$$\begin{bmatrix}-1 & 2\\ 10 & -6\end{bmatrix}$$

D. $$$\begin{bmatrix}0 & 2\\ 10 & -6\end{bmatrix}$$

78. What is $-3A$ if $$A=\begin{bmatrix}-1 & 2\\ 4 & 0\end{bmatrix}?$$

A. $$$\begin{bmatrix}-3 & 6\\ 12 & 0\end{bmatrix}$$

B. $$$\begin{bmatrix}-4 & -1\\ -7 & -3\end{bmatrix}$$

C. $$$\begin{bmatrix}3 & 6\\ -12 & 0\end{bmatrix}$$

D. $$$\begin{bmatrix}3 & -6\\ -12 & 0\end{bmatrix}$$

79. What is $A + B$ for matrices $A$ and $B$ given by $$A=\begin{bmatrix}5 & 0\\ -2 & 1\end{bmatrix},\quad B=\begin{bmatrix}-1 & -3\\ 4 & 2\end{bmatrix}?$$

A. $$$\begin{bmatrix}6 & 3\\ -6 & -1\end{bmatrix}$$

B. $$$\begin{bmatrix}4 & 3\\ -6 & 3\end{bmatrix}$$

C. $$$\begin{bmatrix}4 & -3\\ 2 & 3\end{bmatrix}$$

D. $$$\begin{bmatrix}-5 & 0\\ -8 & 2\end{bmatrix}$$

80. What is the determinant of the matrix $$\begin{bmatrix}-4 & 2\\ 3 & 1\end{bmatrix}?$$

A. $$-2$

B. $$2$

C. $$-10$

D. $$10$

81. If $$A=\begin{bmatrix}0 & -2\\ 5 & 1\end{bmatrix},$$ what is $2A$?

A. $$$\begin{bmatrix}0 & -4\\ 10 & 2\end{bmatrix}$$

B. $$$\begin{bmatrix}0 & -4\\ 5 & 1\end{bmatrix}$$

C. $$$\begin{bmatrix}0 & -1\\ \tfrac{5}{2} & \tfrac{1}{2}\end{bmatrix}$$

D. $$$\begin{bmatrix}0 & 4\\ -10 & -2\end{bmatrix}$$

82. Two $2\times2$ matrices summarize changes in inventory: $A=[ -3, 2 , 5, -1 ]$ and $B=[ 4, -2 , -1, 3 ]$. What is $A+B$?

A. $$[[1,-4],[6,2]]$

B. $$[[ -7, 4 ],[ 6, -4 ]]$

C. $$[[1,0],[4,2]]$

D. $$[[ -1, 0 ],[ 4, 2 ]]$

83. What is kA if $k = 3$ and $A = \begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix}$?

A. $$\begin{bmatrix} 5 & -2 \\ 0 & 12 \end{bmatrix}$

B. $$\begin{bmatrix} 6 & 3 \\ 0 & 8 \end{bmatrix}$

C. $$\begin{bmatrix} 6 & -3 \\ 0 & 12 \end{bmatrix}$

D. $$\begin{bmatrix} 6 & -1 \\ 0 & 4 \end{bmatrix}$

84. What is the determinant of matrix $\begin{bmatrix} 5 & 2 \\ -1 & 3 \end{bmatrix}$?

A. 13

B. 15

C. 17

D. 21

85. What is the determinant of matrix $\begin{bmatrix} 1 & 3 \\ -2 & 0 \end{bmatrix}$?

A. -6

B. -3

C. 3

D. 6

86. In a game engine, two $2\times2$ matrices are applied in sequence: $A=[1,2,-1,3]$ followed by $B=[0,4,2,-1]$. Which of the following is the product $AB$?

A. $$[[4,2],[6,-7]]$

B. $$[[4,6],[2,-7]]$

C. $$[[4,2],[10,-7]]$

D. $$[[0,8],[-2,-3]]$

87. A $2 \times 2$ matrix represents a linear transformation. What is the determinant of $$\begin{bmatrix} 2 & -5 \\ 1 & 3 \end{bmatrix}$$?

A. $$1$

B. $$-1$

C. $$-11$

D. $$11$

88. If $A = \begin{pmatrix} 2 & 3 \\ 1 & -1 \end{pmatrix}$, what is $4A$?

A. $$\begin{pmatrix} 6 & 8 \\ 2 & -2 \end{pmatrix}$

B. $$\begin{pmatrix} 8 & 12 \\ 4 & -4 \end{pmatrix}$

C. $$\begin{pmatrix} 8 & 3 \\ 1 & -4 \end{pmatrix}$

D. $$\begin{pmatrix} 2 & 12 \\ 4 & -1 \end{pmatrix}$

Next test →