University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2021
Views:

55

Pages:

5
Author:

larbiwxcvbn

Algebra 2 Honors Matrices Test Review Name______________________ Date_______________________ Sketch the system and estimate the solutions. 1. 𝑥 2 + 5 = 𝑦 2. 4𝑥 2 + 𝑦 2 = 16 𝑥+𝑦=4 𝑦 = 𝑥2 − 2 3. 𝑦 = 𝑥 2 − 2𝑥 𝑥 = 2𝑦 2 6. 4𝑥 2 + 𝑦 2 = 16 𝑥2 + 𝑦2 = 7 Solve the system of equations. 4. 𝑦 = 𝑥2 − 3 𝑦 = 2𝑥 7. 𝑥 + 2𝑦 − 𝑧 = 5 2𝑥 − 𝑦 + 𝑧 = 2 3𝑥 + 𝑦 + 2𝑧 = 5 5. 𝑥2 − 𝑦2 = 8 𝑥 − 3𝑦 = 0 8. 2𝑥 − 2𝑦 + 𝑧 = −3 𝑥 + 𝑦 − 𝑧 = −4 3𝑥 + 2𝑦 + 2𝑧 = 2 Use the following matrices to perform the indicated operation, or explain why it cannot be done. 𝐴 = [2 9. 1 0 −1] 𝐵 = [ −2 2 1 4 ] 0 0 𝐶=[ 2 −2 3 −1] 1 1 𝐷 = [0 2 4 −1] 0 𝐸=[ 2 −5 −1 ] 6 10. 𝐺 2 3𝐸 − 4𝐺 4 𝐹 = [−1 7 0 1 5 2 0] 0 𝐺=[ 4 2 −3 ] 0 11. 𝐶𝐵 Use the following matrices to solve the matrix equation for the unknown matrix, X, or show that no solution exists. 2 𝐴=[ 3 1 ] 2 𝐵=[ 1 −2 ] −2 4 1 (𝑋 2 𝐶=[ 0 1 −2 4 12. 𝐴 + 3𝑋 = 𝐵 13. − 2𝐵) = 𝐴 15. 2𝑋 + 𝐶 = 5𝐴 16. 𝐴 + 2𝑋 = 𝐷 3 ] 0 5 𝐷=[ 2 0 −1 ] −3 1 14. 2(𝑋 − 𝐴) = 3𝐵 17. 𝐶 − 4𝑋 = 𝐷 Evaluate. Determine if an inverse will exist. Be sure that you can do the problem by hand and on the graphing calculator. 3 −4 15 2 −5 4 18. | 19. | 20. | | | | 5 −6 −1 −3 −6 0 Evaluate. Determine if an inverse will exist. Be sure that you can do the problem by hand and on the graphing calculator. 3 0 −1 2 −4 0 −1 2 3 21. | 2 −3 0 | 22. |−1 1 23. |−2 −4 5 | 2| −4 −2 1 0 −3 −2 −2 5 −6 Find the inverse of each matrix. If the matrix has no inverse, say so. 7 2 5 −7 24. [ 25. [ ] ] −1 0 −3 4 26. [ 4 10 ] 2 5 Solve the system of equations using matrices. 2x2 must be done by hand, 3x3 can be done on the calculator. 27. 12𝑥 − 5𝑦 = 10 5𝑥 − 2𝑦 = 17 28. 6𝑥 − 5𝑦 = 1 8𝑥 − 7𝑦 = −1 1 2𝑥 + 𝑦 + 5𝑧 = 3 1 29. 𝑥 + 2𝑦 + 2𝑧 = 4 𝑥+ 1 3𝑧 = 6 2𝑥 + 3𝑧 = 5 30. 𝑥 + 𝑦 + 6𝑧 = 0 3𝑥 − 𝑦 + 𝑧 = 5 Solve the system using Cramer’s Rule. 2x2 must be done by hand, 3x3 can be done on the calculator. 31. 2𝑥 + 7𝑦 = 13 6𝑥 + 16𝑦 = 30 32. 12𝑥 − 11𝑦 = 140 7𝑥 + 9𝑦 = 20 33. 3𝑥 − 2𝑦 = 4 −6𝑥 + 4𝑦 = 7 34. 5𝑥 + 2𝑦 = 3 −10𝑥 − 4𝑦 = −6 35. 2𝑥 − 𝑦 + 5𝑧 = 0 −𝑥 + 7𝑦 =9 5𝑥 + 4𝑦 + 3𝑧 = −9 3𝑥 + 4𝑦 − 𝑧 = 10 − 4𝑧 = 20 36. 𝑥 2𝑥 + 𝑦 + 5𝑧 = 30 Answers 1. No Solution 2. (−2, 1.5)(2, 1.5) 3. (0,0)(2.5, 1.2)(2.5, −1.2) 6. (±√3, ±2) 4. (3, 6)(−1, −2) 5. (3, 1)(3, −1) 8. (−2, 1, 3) 9. [ 1 − −1 12. [ 35 2 ] −3 3 13. [ −10 9 ] −23 18 10. [ 6 −2 ] 2 12 14. [ 2 0 5 1 −2 ] 8 −6 3 0 11. [ 4 3 8] −4 −3 −8 15. Not Possible 19. 2, 𝑌𝑒𝑠 21. 7, 𝑌𝑒𝑠 22. 16, 𝑌𝑒𝑠 23. −97, 𝑌𝑒𝑠 0 −1 25. [ 1 7 ] 26. No Inverse Exists 27. [ 10 30. [ 20 ] −5 31. ( , ) 34. Infinite Solutions 35. (− 26 , 26 , 2) 17. [ 20. 24, 𝑌𝑒𝑠 −4 −7 ] −3 −5 7 (2, 1, −1) 18. −43, 𝑌𝑒𝑠 16. Not Possible 24. [ 1 4 7 4 −4 10 −12 ] 8 −6 7. −1 2 1] −4 2 65 ] 154 1 − 12 6 28. [ ] 7 29. [ 32. (8, −4) 860 36. ( 41 , − 1 12 1 12 ] 33. No Solution 540 10 , ) 41 41 1 9 5 5 87 21 3