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of Linear Equations and 22. A = [²29]

of Linear Equations and 22. A = [²29]

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
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1.4 19 and 22 please on paper ( theyr very short thank youu)
52 CHAPTER 1 Systems of Linear Equations and Matrices 21. A = 12² 11 22. A = 9 In Exercises 23-24, let a b A = = [₁ 2] B = [3] c = [₁] C 23. Find all values of a, b, c, and d (if any) for which the matrices A and B commute. In a 24. Find all values of a, b, c, and d (if any) for which the matrices A and C commute. 3 In Exercises 25-28, use the method of Example 8 to find the unique solution of the given linear system. 25. 3x₁ - 2x₂ = -1 26. x₁ + 5x₂ = 4 4x₁ + 5x₂ = 3 -X₁ - 3x₂ = 1 . 6x₁ + x₂ = 28. 2x₁2x₂ = 4 4x₁ - 3x₂ = -2 X₁ + 4x₂ = 4 = polynomial p(x) can be factored as a product of lower degree nomials, say p(x) = P₁(x)p₂(x) fA is a square matrix, then it can be proved that p(A) = P₁(A)p₂(A) ercises 29-30, verify this statement for the stated 36. In E the ent 37
Transcribed Image Text:52 CHAPTER 1 Systems of Linear Equations and Matrices 21. A = 12² 11 22. A = 9 In Exercises 23-24, let a b A = = [₁ 2] B = [3] c = [₁] C 23. Find all values of a, b, c, and d (if any) for which the matrices A and B commute. In a 24. Find all values of a, b, c, and d (if any) for which the matrices A and C commute. 3 In Exercises 25-28, use the method of Example 8 to find the unique solution of the given linear system. 25. 3x₁ - 2x₂ = -1 26. x₁ + 5x₂ = 4 4x₁ + 5x₂ = 3 -X₁ - 3x₂ = 1 . 6x₁ + x₂ = 28. 2x₁2x₂ = 4 4x₁ - 3x₂ = -2 X₁ + 4x₂ = 4 = polynomial p(x) can be factored as a product of lower degree nomials, say p(x) = P₁(x)p₂(x) fA is a square matrix, then it can be proved that p(A) = P₁(A)p₂(A) ercises 29-30, verify this statement for the stated 36. In E the ent 37
10. Find the inverse of cos e sin e 1 - sine cose In Exercises 11-14, verify that the equations are valid for the matri- ces in Exercises 5-8. 11. (AT)-¹ = (A-¹)T 12. (A-¹)-¹ = A 13. (ABC)-¹ = C-¹B-¹A-¹ 14. (ABC) = CTBTAT In Exercises 15-18, use the given information to find A. -3 15. (74)-¹ = [2] 16. (SAT)-¹ = [3 1 5 LOW! -1 17. (I + 2A)-¹; = em 18. A-¹ = -3 4 5 1110 In Exercises 19-20, compute the following using the given matrix A. (01 a. A³ b. A-3 c. A² - 2A +I 19. A = =[2₂1] 20. A = In Exercises 21-22, compute p(A) for the given matrix A and the following polynomials. a. p(x) = x - 2 b. p(x) = 2x²-x+1 c. p(x) = x³ - 2x + 1 141 2]
Transcribed Image Text:10. Find the inverse of cos e sin e 1 - sine cose In Exercises 11-14, verify that the equations are valid for the matri- ces in Exercises 5-8. 11. (AT)-¹ = (A-¹)T 12. (A-¹)-¹ = A 13. (ABC)-¹ = C-¹B-¹A-¹ 14. (ABC) = CTBTAT In Exercises 15-18, use the given information to find A. -3 15. (74)-¹ = [2] 16. (SAT)-¹ = [3 1 5 LOW! -1 17. (I + 2A)-¹; = em 18. A-¹ = -3 4 5 1110 In Exercises 19-20, compute the following using the given matrix A. (01 a. A³ b. A-3 c. A² - 2A +I 19. A = =[2₂1] 20. A = In Exercises 21-22, compute p(A) for the given matrix A and the following polynomials. a. p(x) = x - 2 b. p(x) = 2x²-x+1 c. p(x) = x³ - 2x + 1 141 2]
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