Algebra 2 Review Chapter 4 Name __________________________________ 1. Use the table for Exercises a, b, and c Construction Manufacturing Transportation Sales Finance Services Government a. Display the data in a 2 x 7 matrix. June, 1992 17.6% 8.3% 5.4% 8.7% 4.0% 6.6% 3.5% b. State the dimensions of the matrix. c. Identify a 21 and tell what it represents. Find each sum or difference. 2. 4. 4 7 9 3 2 1 6 0 Find the product. 3. 4 5 1 7 10 4 10 7 4 17 0 3 21 9 6 2 6 1 6. 2 0 5 10 2X 1 4 15 9 2 6 1 5 1 0 3 1 Solve each matrix equation. 5. 3 8 2 8 10 5 X 1 12 7. Find the values for x and z.. 8. Solve for X. 13 2 x 1 4x 5 1 2 0 2 10 10 5 z 2.5 z x 3 2 10 11 1 5 X 26 36 9. Find the dimensions of the product matrix. Then find each product. 1 2 2 1 a. 2 1 1 2 1 b. 2 1 2 3 4 3 c. 8 5 1 2 0 9 7 June, 1996 9.5% 5.1% 4.5% 6.4% 2.6% 5.1% 2.7% 10. Parallelogram ABCD has coordinates A(2,-1), B(4,3), C(1,5), and D(-1,1). Write a matrix for the vertices of its image after each transformation. a. a dilation of size 2 3 b. reflection in y = x 11. Triangle ABC has coordinates A((4, 2), B(4, -2), and C(-3, 0). Find the coordinates of the image under each transformation. Express your answer as a matrix. a. a reflection in the x-axis b. a translation 1 unit left and 2 units down c. a rotation of 90 12. Use an inverse matrix to solve each equation or system. a. 3 5 2 6 6 2 X 4 12 b. x y 3 2 x y 1 c. Find the inverse of each matrix if it exists. If it does not exist, write no inverse. 13. a. 4 7 E 3 5 b. J= 3 4 3 4 Find the determinant of each matrix. 14. a. 8 3 2 9 b. 0.5 1 3 0 Solve each system. Show your work. 15. x y z 31 a. x y z 1 x 2 y 2z 7 b. 3 x 4 y 2 x y 1 16. Explain how to determine whether two matrices can be multiplied and what the dimensions of the product matrix will be. 17. Are these matrices inverses of each other? a. 3 2 3 2 4 3 , 4 3 b. 3 7 5 7 2 5 , 2 3 18. An apartment building has 50 units. All are one- or two- bedroom units. One-bedroom units rent for $425/mo, and twobedroom units rent for $550/mo. When all units are occupied, the total monthly income is $25,000. How many apartments of each type are there?