Name: Class: Date: ID: A Algebra 2 - Review - Unit Matrices Short Answer Determine whether the product is defined or undefined. If defined, give the dimensions of the product matrix. 1. 2. 5 1 7 9 2 1 1 5 6 0 9 1 7. Find the dimensions of the matrix. 1 2 5 0 5 0 9 7 9 12 8 1 8 5 0 6 Identify the given matrix element.. a, 2 1 2 5 5 0 7 9 6 1 8 5 2 1 Find the values of the variables. 5. + t 0 8 10 = 5 0 8 2y + 2 1
Name: ID: A 6. 1 15 + 10 6 2 21 = x 0 x 2y + 28 5y + 10 7. The Art Department and the Homecoming Committee at a local school are ordering supplies. The supplies they need are listed in the table. Paint (bottles) Brushes Paper (reams) Glue Sticks (boxes) Tape (rolls) Art Department 11 12 11 Homecoming Committee 10 1 7 17 7 A bottle of paint costs $, a paint brush costs $2, a ream of colored paper costs $8, a box of glue sticks costs $, and a roll of tape costs $2. Find the matrix that represents the total cost of supplies for each group. Use matrices A, B, and C. Find the sum or difference if you can. A = 5 8. C + A 8 2 B = 2 7 1 6 0 C = 9. Find 7A + 2B for the following matrices: A = 9 6 5 2 B = Solve the matrix equation. 9 8 9 8 1 5 1 0 6 10. X + 2 2 8 2 = 6 2 8 What is the solution of the matrix equation? 11. 5 2 X = 2
Name: ID: A Evaluate the determinant of the matrix. 12. 1. 1. 1 9 2 6 1 1 2 2 1 2 1 2 5 1 6 7 Evaluate the determinant. 15. 5 2 5 16. One factor in flood safety along a levee is the area that will absorb water should the levee break. The coordinates that make up the boundary area are Ê Ë Á 0,0 ˆ, Ê Ë Á2.,1. ˆ, and Ê ËÁ.,.9 ˆ. What is the area of the land that would absorb the water? Determine whether the matrix has an inverse. If an inverse exists, find it. 17. 18. 5 18 2 7 0 7 0 19. A = 1 1 2
Name: ID: A 20. Ï 7y 9z = 8 Write the system Ì Ô 5x y = 6 as a matrix equation. ÓÔ 7x + 6z = 6 Solve the system. 21. 22. 2. Ï 7x + 2y = 2 Ì Ô ÓÔ 11x y = 5 Ï 5x + 2y = 10 Ì Ô 2y z = 15 ÓÔ 5x + z = 5 Ï x + y + z = 22 Ì Ô 2x + 5y z = ÓÔ 5x + 2y + 5z = 1
Name: ID: A Essay 2. The following tables show car and SUV sales for a dealership in 1990 and 2000. The months shown represent the end of each quarter. Sales in 1990 March June September December SUVs 60 26 77 Cars 128 201 179 11 Sales in 2000 March June September December SUVs 110 66 80 118 Cars 122 188 176 99 a. Organize the information into two 2 x matrices, A (1990) and B (2000). b. Calculate the matrix that shows the change in sales from 1990 to 2000. c. For which type of vehicle did sales increase? Explain. 25. The matrix x 2 has no inverse. Explain how you can determine the value of x. Then find x. 5
ID: A Algebra 2 - Review - Unit Matrices Answer Section SHORT ANSWER 1. ANS: undefined OBJ: 12-2.1 To multiply matrices using scalar and matrix multiplication 2. ANS: defined; 2 1 OBJ: -.2 Multiplying Matrices. ANS: OBJ: -1.1 Identifying Matrices. ANS: 5 OBJ: -1.1 Identifying Matrices 5. ANS: t = 8, y = 6 OBJ: -2.2 Solving Matrix Equations 6. ANS: x = 7 and y = 2 OBJ: 12-1.1 To add and subtract matrices and to solve matrix equations 7. ANS: 11 189 OBJ: -.2 Multiplying Matrices 8. ANS: not possible OBJ: 12-1.1 To add and subtract matrices and to solve matrix equations 9. ANS: 7 9 51 16 OBJ: 12-2.1 To multiply matrices using scalar and matrix multiplication 1
ID: A 10. ANS: 0 10 10 12 OBJ: 12-2.1 To multiply matrices using scalar and matrix multiplication 11. ANS: 1 OBJ: 12-.1 To solve systems of equations using matrix inverses and multiplication 12. ANS: 1 OBJ: -5.1 Evaluating Determinants of 2 x 2 Matrices 1. ANS: OBJ: 12-.1 To find the inverse of a matrix 1. ANS: 29 OBJ: 12-.1 To find the inverse of a matrix 15. ANS: OBJ: -5.1 Evaluating Determinants of 2 x 2 Matrices 16. ANS: 1.6 mi 2 OBJ: 12-.1 To find the inverse of a matrix 17. ANS: 7 18 2 5 OBJ: -5.1 Evaluating Determinants of 2 x 2 Matrices 18. ANS: does not exist OBJ: -5.1 Evaluating Determinants of 2 x 2 Matrices 2
ID: A 19. ANS: 1 2 1 OBJ: 12-.1 To find the inverse of a matrix 20. ANS: 0 7 9 x 8 5 0 7 0 6 y z = 6 6 OBJ: 12-.1 To solve systems of equations using matrix inverses and multiplication 21. ANS: 16 57 OBJ: 12-.1 To solve systems of equations using matrix inverses and multiplication 22. ANS: no unique solution OBJ: -8.2 Solving Systems Using Augmented Matrices 2. ANS: (5, 2, ) OBJ: 12-.1 To solve systems of equations using matrix inverses and multiplication
ID: A ESSAY 2. ANS: [] a. A = b. 60 26 77 128 201 179 11 50 5 1 6 1 15, B = 110 66 80 118 122 188 176 99 c. SUVs; the row representing the changes in SUV sales are all positive numbers, whereas those for car sales are all negative. [] only three of four answers (three matrices, one explanation) correct [2] only two of four answers correct [1] only one of four answer correct OBJ: -2.1 Adding and Subtracting Matrices OTHER 25. ANS: Since the matrix has no inverse, its determinant is 0. So Ê 2 ˆ ËÁ x = 0. Solving for x, x = 1 2. OBJ: -5.1 Evaluating Determinants of 2 x 2 Matrices