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1. Provide detail justifications for the following questions about the linear system: (2x + 2y + z = 1 -y+z=2 +z=2 a) Express the above linear system in matrix form as Ax = b. Give the matrices A,x and b. b) For the above linear system, it is given that the coefficient matrix is invertible, and: -1 -2 3 A-¹ = 1 1 -2. 1 2 Find the solution to the linear system using the inverse matrix. c) Explain the method of Gauss Elimination to find the solution of the linear system Ax = b. Solve the given linear system, using the method of Gauss elimination. D

1. Provide detail justifications for the following questions about the linear system: (2x + 2y + z = 1 -y+z=2 +z=2 a) Express the above linear system in matrix form as Ax = b. Give the matrices A,x and b. b) For the above linear system, it is given that the coefficient matrix is invertible, and: -1 -2 3 A-¹ = 1 1 -2. 1 2 Find the solution to the linear system using the inverse matrix. c) Explain the method of Gauss Elimination to find the solution of the linear system Ax = b. Solve the given linear system, using the method of Gauss elimination. D

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 32E
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1. Provide detail justifications for the following questions about the linear system: (2x +2y + z = 1 -y+z=2 +z=2 a) Express the above linear system in matrix form as Ax = b. Give the matrices A,x and b. b) For the above linear system, it is given that the coefficient matrix is invertible, and: 3 -1 -2 A¹ = 1 1 -2 2 -2 Find the solution to the linear system using the inverse matrix. c) Explain the method of Gauss Elimination to find the solution of the linear system Ax = b. Solve the given linear system, using the method of Gauss elimination. d) Explain the advantages of the method of Gauss-Jordan elimination. Solution:
Transcribed Image Text:1. Provide detail justifications for the following questions about the linear system: (2x +2y + z = 1 -y+z=2 +z=2 a) Express the above linear system in matrix form as Ax = b. Give the matrices A,x and b. b) For the above linear system, it is given that the coefficient matrix is invertible, and: 3 -1 -2 A¹ = 1 1 -2 2 -2 Find the solution to the linear system using the inverse matrix. c) Explain the method of Gauss Elimination to find the solution of the linear system Ax = b. Solve the given linear system, using the method of Gauss elimination. d) Explain the advantages of the method of Gauss-Jordan elimination. Solution:
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