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5. 6. ) Perform LU decomposition and verify that LU = A ) Solve the system using your LU decomposition and verify your solution from nart 4

5. 6. ) Perform LU decomposition and verify that LU = A ) Solve the system using your LU decomposition and verify your solution from nart 4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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Question

please answer 5,6 make sure write this by hand in clear page

For the following systems of equations: 1. ( 2. 3. 4. 5. 6. ) Write the system as Ax = b and form the augmented matrix (Alb) ) Calculate det(A) and state whether the system has a unique solution ) Use Gaussian elimination to calculate REF of A and (Alb), state the rank of A and (Alb), and state how many solutions the system has. ) Use Gauss-Jordan elimination to calculate RREF of (AI) and (Alb) to find A-¹ and x, respectively ) Perform LU decomposition and verify that LU = A ) Solve the system using your LU decomposition and verify your solution from part 4.
Transcribed Image Text:For the following systems of equations: 1. ( 2. 3. 4. 5. 6. ) Write the system as Ax = b and form the augmented matrix (Alb) ) Calculate det(A) and state whether the system has a unique solution ) Use Gaussian elimination to calculate REF of A and (Alb), state the rank of A and (Alb), and state how many solutions the system has. ) Use Gauss-Jordan elimination to calculate RREF of (AI) and (Alb) to find A-¹ and x, respectively ) Perform LU decomposition and verify that LU = A ) Solve the system using your LU decomposition and verify your solution from part 4.
System 1: System 2: 2x₁ + 2x₂x3 = -2 -x₁ = 1 2x₁ + 2x₂ + 2x3 = 4 x₁2x₂ - 2x3 = 6 -x₁ - x₂ + - = = -4
Transcribed Image Text:System 1: System 2: 2x₁ + 2x₂x3 = -2 -x₁ = 1 2x₁ + 2x₂ + 2x3 = 4 x₁2x₂ - 2x3 = 6 -x₁ - x₂ + - = = -4
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