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1 2. [1 2 01 1 1 4 a. 66 +3 1 b. 0 1 0 c. 0 0 1 000 20 0 0 0 [1 5 [1 2 3] d. 0 1 e. 0 0 0 0 0 0 0 2 3 4 51 1071 3 1 -2 6 0 0001 0 00000 f. ga 0 1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 23EQ
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Questions 2 Q,5,6,7,8 On Paper please
d. 0 1 0 0 In Exercises 5-8, solve the system by Gaussian elimination. 5. x₁ + x₂ + 2x3 = 8 -X₁ - 2x₂ + 3x3 = 1 3x₁ - 7x₂ + 4x3 = 10 6. 2x₁ + 2x₂ + 2x3 = 1902-2x₁ + 5x2 + 2x3 = 8x₁ + x₂ + 4x3 = -1 x = y + 2z - w = -1 2x + y2z - 2w = -2 -x + 2y - 4z + w = 1 3x - 3w = -3 - 2b + 3c = 1 3a +6b- 3c = -2 6a+ 6b+ 3c = 5 In Exercises 9-12, solve the system by Gauss-Jordan elimination. 7. 8. 22. In ec ear s real whe eno 23. 24
Transcribed Image Text:d. 0 1 0 0 In Exercises 5-8, solve the system by Gaussian elimination. 5. x₁ + x₂ + 2x3 = 8 -X₁ - 2x₂ + 3x3 = 1 3x₁ - 7x₂ + 4x3 = 10 6. 2x₁ + 2x₂ + 2x3 = 1902-2x₁ + 5x2 + 2x3 = 8x₁ + x₂ + 4x3 = -1 x = y + 2z - w = -1 2x + y2z - 2w = -2 -x + 2y - 4z + w = 1 3x - 3w = -3 - 2b + 3c = 1 3a +6b- 3c = -2 6a+ 6b+ 3c = 5 In Exercises 9-12, solve the system by Gauss-Jordan elimination. 7. 8. 22. In ec ear s real whe eno 23. 24
Exercise Set 1.2 In Exercises 1-2, determine whether the matrix is in row echelon form, reduced row echelon form, both, or neither. 2. 1 0 0 [1 0 0 0 1 0 1. a. 0 1 0 b. 0 1 0 C. 0 0 1 0 0 1 0 0 0 0 0 d. 0 1 0 69 0 0 f. 32 LO 0 There is often a gap between mathematical theory and its practical implementation- Gauss-Jordan elimination and Gaussian elimination being good examples. The problem is that computers generally approximate numbers, thereby introducing roundoff errors, so unless precautions are taken, successive calculations may degrade an answer to a degree that makes it useless. Algorithms in which this happens are called unstable. There are various techniques for minimizing roundoff error and instability. For example, it can be shown that for large linear systems Gauss-Jordan elimination involves roughly 50% more operations than Gaussian elimination, so most computer algorithms are based on the lat- ter method. Some of these matters will be considered in Chapter 9. [1 2 0 1 0 0 1 3 010 b. 0 1 0 0 0 0 0 0 020 0 0 1 0 0 1 1 0 0 e. 0 0 LO .. 0 g. [1 2 0 3 0 1 0 0 0 0 0 5 1 3 BLOO 1 0 0 810 0 52 a. d. f. 5 -3 1 1 0 0 2 3 4 0 7 1 0 0 0 0 0 0 5 3 1 0 e. on C. [1 2 3 0 0 0 0 0 1 1 -2 0 0 1 0 0 1 1 -2
Transcribed Image Text:Exercise Set 1.2 In Exercises 1-2, determine whether the matrix is in row echelon form, reduced row echelon form, both, or neither. 2. 1 0 0 [1 0 0 0 1 0 1. a. 0 1 0 b. 0 1 0 C. 0 0 1 0 0 1 0 0 0 0 0 d. 0 1 0 69 0 0 f. 32 LO 0 There is often a gap between mathematical theory and its practical implementation- Gauss-Jordan elimination and Gaussian elimination being good examples. The problem is that computers generally approximate numbers, thereby introducing roundoff errors, so unless precautions are taken, successive calculations may degrade an answer to a degree that makes it useless. Algorithms in which this happens are called unstable. There are various techniques for minimizing roundoff error and instability. For example, it can be shown that for large linear systems Gauss-Jordan elimination involves roughly 50% more operations than Gaussian elimination, so most computer algorithms are based on the lat- ter method. Some of these matters will be considered in Chapter 9. [1 2 0 1 0 0 1 3 010 b. 0 1 0 0 0 0 0 0 020 0 0 1 0 0 1 1 0 0 e. 0 0 LO .. 0 g. [1 2 0 3 0 1 0 0 0 0 0 5 1 3 BLOO 1 0 0 810 0 52 a. d. f. 5 -3 1 1 0 0 2 3 4 0 7 1 0 0 0 0 0 0 5 3 1 0 e. on C. [1 2 3 0 0 0 0 0 1 1 -2 0 0 1 0 0 1 1 -2
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