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Name: _______________________________ Period: _______ Date: _______________ REVIEW 4-1 to 4-5 State the dimensions of each matrix. 1. é 0 -4 7 -2 ù ê 8 5 6 2 ú ê ú êë 4 -2 3 -5 úû 2. [ -3 -3 7] Solve each equation. 3. [ -2x 22 -3z ] = [ 6x -2y 45 ] 5. é -5 3x + 1 ù é -5 x - 1 ù ê 2y - 1 3z - 2 ú = ê 3y 5z - 4 ú ë û ë û 4. é 7x - 8 ù é 20 ù ê -3y + 6 ú = ê 2y + 3 ú ë û ë û 6. é 2x + y ù é 0 ù ê 3x + 2y ú = ê -2 ú ë û ë û 7. The table gives ticket prices for a concert. Write a 2 x 3 that represents the cost of a ticket. Cost Purchased in Advance. Cost Purchased at the Door Child $6 Student $12 Adult $18 $8 $15 $22 Perform the indicated matrix operations. If the matrix does not exist, write impossible. 8. é 2 -1 8 ù é -1 4 -3 ù 7ê - 2 ê ú ú ë 4 7 9 û ë 7 2 -6 û 9. 3 é 8 12 ù 2 é 27 -9 ù + 4 êë -16 20 úû 3 êë 54 -18 úû é1 ù é 0 ù é10 ù -2 ê ú + 4 ê ú - ê ú ë2 û ë 5 û ë18 û 10. é 4 -1 0 ù é -2 4 5 ù ê -3 6 2 ú ê ú û , B = ë 1 0 -9 û , and C = Use A = ë following. 11. -3b 12. -2b – 3c é10 -8 6 ù ê -6 -4 20 ú ë û to find the 13. A + 0.5C ECONOMICS. For Exercises 14 and 15, use the table that shows loans by an economic development board to women and men starting new businesses. 1999 2000 2001 Women Businesses Loan Amt ($) 27 $567,000 41 $902,000 35 $777,000 Businesses 36 32 28 Men Loan Amt ($) $864,000 $672,000 $562,000 14. Write two matrices that represent the number of new businesses and loan amounts, one for women and one for men. 15. Find the sum of the numbers of new businesses and loan amounts for both men and women over the three-year period expressed as a matrix. Determine whether each matrix product is defined. If so, state the dimensions of the product. 16 . A3x5 * B5x8 17. M3x2 * A3x2 18. P9x1 * Q1x9 Find each product, if possible. If it is not possible, write impossible. é 3 -2 7 ù é 3 -2 7 ù ê 6 0 -5 ú · ê 6 0 -5 ú û ë û 18. ë é 1 ù [ 4 0 2 ] · êê 3úú êë -1 úû 20. 19. é 1 ù ê 3ú · 4 0 2 ] ê ú [ êë -1 úû RENTALS. For exercises 21 – 23, use the following information. For their one-week vacation, the Montoyas can rent a 2-bedroom condominium for $1,796, a 3-bedroom condominium for $2,165, or a 4-bedroom condominium for $2,538. The table shows the number of units in each of three complexes. Sun Haven Surfside Seabreeze 2-Bedroom 36 29 18 3-Bedroom 24 32 22 4-Bedroom 22 42 18 21. Write a matrix that represents the number of each type of unit available at each complex and a matrix that represents the weekly charge for each type of unit. 22. If all of the units in the three complexes are rented for the week at the rates given the Montoyas, express the income of each of the three complexes as a matrix. 23. What is the total income of all three complexes for the week? Find the value of each determinant. 24. 4 1 -2 -5 25. 2 -1 3 -9.5 26. 0.5 -0.7 0.4 -0.3 Evaluate each determinant using expansion by minors. 27. 2 -4 1 2 7 -6 3 0 9 8 4 0 -1 5 7 28. 1 -1 3 Evaluate each determinant using diagonals. 29. 1 2 -4 2 1 3 1 4 -6 1 8 0 2 3 3 30. 0 5 -1 31. Find the area of a triangle whose vertices have coordinates (3, 5), (6, -5), and (-4, 10).