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Precalculus Name: Period: Date: Chapter 7 Review Test 1. In the following system of equations, solve for X and Y using substitution (must show work or NO credit): 1. 2.5X + 4Y = 13 X - 4Y = 8 2. In the following system of equations, solve for X and Y using elimination (must show work or NO credit): Y = _______ 2. 2X + 4Y = 7 -X + 3Y = 4 3. In the following system of equations, solve for X and Y using any method: 2X - 5Y = 10 3X + 4Y = 9 X = _______ X = _______ Y = _______ 3. X = _______ Y = _______ 4. State how many solutions exist for the following systems: a. 2X + 5Y = 10 and X + 6Y = -5 4a. _______ b. 3Y + X = 2 and .5Y + (X/6) = 1/3 4b. _______ c. 4Y + X = 3 and -10Y + 3X = -9 4c. _______ d. X2 + Y2 = 25 and Y = 2X2 -5X -3 4d. _______ ( x) 2 ( y 3) 2 e. 1 and 16 9 4e. _______ 5. Write the order of the following matrices 2 3 6 8 4 7 .5 1/ 3 a. b. 2 5a. _______ 0 5 5b. _______ For questions 6 – 9 and 12 use the following matrices: 3 2 A 6 5 5 1 2 B 3 4 4 0 .5 C 4 2 0 1 3 D 4 2 5 6 10 4 6. Perform the following operations (if the operation is not possible write N/A): a. A - C 6a. ________________ b. 3A + 1/2C 6b. ________________ c. 1/5(BD) 6c. ________________ d. AB + CB 6d. ________________ 7. Verify if B and D are inverses of each other and state your reasoning 7 Inverses Y or N (Circle one) Reasons__________________ _________________________ 8. Determine the inverse of C without using the calculator Inverse function (must show work or NO credit): 8 ______________________ 9. Determine the inverse of D (round to 2 decimals) (you may use any method you like) 9 ______________________ 10. Solve the following system of equations (you must use matrix operations) -- (must show work or NO credit): 5X + 3Y = -7 .4X - .6Y = 2/3 Matrix Set up: Inverse Matrix (round to 4 decimals) Solution (round to 2 decimals): X = ________ Y = ________ 11. (EC) Solve the following system of equations (method of your choice) 5X -3Y + 2Z = 2 3X + 4Z = 3 -X + 7Y - .8Z = 4 11. X = ______ Y = ______ Z = ______ 12. Determine the determinant for C (see previous pages for C) leave answer as a fraction 13. (EC) Determine PXQ for the following vectors: State answer in component form P = 10i, 0j, 5k Q = 3i, -2j, 2k 12. ____________ 13 ___________________