Explanation Given: The system of equations are, 2.1 x 1 − 3.2 x 2 + 6.4 x 3 + 7 x 4 − 3.2 x 5 = 54.3 4.1 x 1 + 2.2 x 2 − 3.1 x 3 − 4.2 x 4 + 3.3 x 5 = − 20.81 3.4 x 1 − 6.2 x 2 + 4.7 x 3 + 2.1 x 4 − 5.3 x 5 = 24.7 4.1 x 1 + 7.3 x 2 + 5.2 x 3 + 6.1 x 4 − 8.2 x 5 = 29.25 2.8 x 1 + 5.2 x 2 + 3.1 x 3 + 5.4 x 4 + 3.8 x 5 = 43.72 Approach: The inverse of the matrix based on Gauss-Jordan method. [ A | B ] → [ I | X ] Here, [ A | B ] is the argument matrix, X is the solution of the given system of equation, I is the identity matrix. Calculation: Consider the given linear equations, 2.1 x 1 − 3.2 x 2 + 6.4 x 3 + 7 x 4 − 3.2 x 5 = 54.3 4.1 x 1 + 2.2 x 2 − 3.1 x 3 − 4.2 x 4 + 3.3 x 5 = − 20.81 3.4 x 1 − 6.2 x 2 + 4.7 x 3 + 2.1 x 4 − 5.3 x 5 = 24.7 4.1 x 1 + 7.3 x 2 + 5.2 x 3 + 6.1 x 4 − 8.2 x 5 = 29.25 2.8 x 1 + 5.2 x 2 + 3.1 x 3 + 5.4 x 4 + 3.8 x 5 = 43.72 The argument matrix is given as follow, [ 2.1 − 3.2 6.4 7 − 3.2 4.1 2.2 − 3.1 − 4.2 3.3 3.4 − 6.2 4.7 2.1 − 5.3 4.1 7.3 5.2 6.1 − 8.2 2.8 5.2 3.1 5.4 3.8 | 54.3 − 20.81 24.7 29.25 43.72 ] Use the Gauss-Jordan method to calculate [ I | X ] as follows, [ 2.1 − 3.2 6.4 7 − 3.2 4.1 2.2 − 3.1 − 4.2 3.3 3.4 − 6.2 4.7 2.1 − 5.3 4.1 7.3 5.2 6.1 − 8.2 2.8 5.2 3.1 5.4 3.8 | 54.3 − 20.81 24.7 29.25 43.72 ] R 1 → R 1 2.1 [ 1 − 1.52 3.05 3.33 − 1.52 4.1 2.2 − 3.1 − 4.2 3.3 3.4 − 6.2 4.7 2.1 − 5.3 4.1 7.3 5.2 6.1 − 8.2 2.8 5.2 3.1 5.4 3.8 | 25.86 − 20.81 24.7 29.25 43.72 ] R 2 → R 2 − 4.1 R 1 R 3 → R 3 − 3.4 R 1 R 4 → R 4 − 4.1 R 1 R 5 → R 5 − 2.8 R 1 [ 1 − 1.52 3.05 3.33 − 1.52 0 8.44 − 15.60 − 17.87 9.55 0 − 1.01 − 5.66 − 9.23 − 0.12 0 13.55 − 7.29 − 7.57 − 1.95 0 9.47 − 5.43 − 3.93 8.07 | 25.86 − 126.82 − 63.21 − 76.76 − 28.68 ] R 2 → R 2 8.44 [ 1 − 1.52 3.05 3.33 − 1.52 0 1 − 15.60 − 17.87 9.55 0 − 1.02 − 5.66 − 9.23 − 0.12 0 13.55 − 7.29 − 7.57 − 1.95 0 9.47 − 5.43 − 3.93 8.07 | 25.86 − 126.82 − 63.21 − 76.76 − 28 To determine b) The solution of the system using the rref operation To determine c) To solve: The system of equations by using SIMULT operation.

12th Edition

ISBN: 8220103649001

Author: Tan

Publisher: CENGAGE L

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Chapter 2.2, Problem 6TE

To determine

a)

To solve:

The system of equations by the Gauss-Jordan method.

To determine

b)

The solution of the system using the rref operation

To determine

c)

To solve:

The system of equations by using SIMULT operation.

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Chapter 2.2, Problem 5TE

Chapter 2.3, Problem 1CQ

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a) To solve: The system of equations by the Gauss-Jordan method.

Solution Summary: The author explains how the Gauss-Jordan method solves the system of equations.

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a) To solve: The system of equations by the Gauss-Jordan method.

b) The solution of the system using the rref operation

c) To solve: The system of equations by using SIMULT operation.

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Chapter 2 Solutions

a)

To solve:

The system of equations by the Gauss-Jordan method.

b)

The solution of the system using the rref operation

c)

To solve:

The system of equations by using SIMULT operation.