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Class:
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Practice TEST Chapter 3 Evaluate the determinant by using diagonals.
Objective Short Answer Determine whether each matrix product is defined. If so, state the dimensions of the product. 1. P9 × 1 • Q1 × 9
7. –1 5
2 –2
2 3
2
3
1
2. Find the inverse of the matrix. 1 4 –4
Find each product, if possible. 8.
–2
Find the product, if possible. 3. 5 7 3 · –3 6 5
8 3
4. Use
and
Solve each system of equations. 10. 3x – 4y = 12
to determine
whether AB = BA for the given matrices. Find the value of the determinant. 5. 4 –2 –1
Solve each system of equations. 9. 8x + 3y = –5 10x + 6y = –13
–3
Use Cramer’s rule to solve the system of equations. 6. –4x – 3y = –38 7x – 2y = –6
Solve each system of equations by graphing. 11. 2x – y = 6 x + 2y = –2 Solve each system of inequalities by graphing. 12. x > –2 2y 3x + 6 13. |y| 1 y < x – 1 Solve each system of equations. 14. x – 4y + 3z = –27 2x + 2y – 3z = 22 4z = –16
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Practice TEST Chapter 3 15. x – y + 9z = –27 2x – 4y – z = –1 3x + 6y – 3z = 27 Perform the indicated operations. If the matrix does not exist, write impossible.
Use
,
and c = 3 to determine whether the following equations are true for the given matrices. 22. (A + C)B = B(A + C) Evaluate each determinant.
16.
23.
Determine whether each pair of matrices are inverses.
17. 18. PET NUTRITION Use the table that gives nutritional information for two types of dog food. Find the difference in the percent of protein, fat, and fiber between Mix B and Mix A expressed as a matrix.
24.
Find the inverse of each matrix, if it exists. 25.
Determine whether each matrix product is defined. If so, state the dimensions of the product. 19. A7 × 4 • B4 × 3
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. 26.
20.
Use substitution to solve each system of equations. 27. x + y = 8 –7x + 7y = 28
21.
Solve the system of inequalities by graphing. 28. x > 1 y > 9
Find each product, if possible.
Use the elimination method to solve each system of equations. 29. 4x + 2y = –14 4x – 6y = –6
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Practice TEST Chapter 3 Solve the given system of equations. 30. –3a = –33 6a + 3c = 93 3b + 4c = 24 Perform the indicated matrix operation. 31. 2
9
–5
–3
+
0
6
–2
–8
0
4
–10
–8
32. 4 3
8
–6
–4
–2
Find the product, if possible. 33. 1 6 4 · –5 3 8
9 –1
Evaluate the determinant by using diagonals. 34. –4 4
4 –1
3 2
3
3
1
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Practice TEST Chapter 3 Answer Key
12.
1. 9 × 9 2.
3.
50
61
21
–6
4. No
13.
5. –14 6. (2, 10) 7. 51 8.
9. 10. infinitely many 11. (2, –2)
14. (1, 4, –4) 15. (2, 2, –3)
16.
17.
18. 19. 7 × 3 20. not defined 21. Powered by Cognero
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Practice TEST Chapter 3 22. no
32.
23. 0
12
16
2
4
52
3
4
–48
24. yes 33.
25. 26. one solution; (1, –4)
34. 81
27. (2, 6) 28.
29. (–3, –1) 30. a = 11, b = –4, c = 9 31.
2
12
–6
–7
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