Explanation Proof: Consider the system of equation 2 x 1 − 3 x 2 = r x 1 x 1 − 2 x 2 = r x 2 Rearrange the system of equation; ( 2 − r ) x 1 − 3 x 2 = 0 ... ( 1 ) x 1 − ( 2 + r ) x 2 = 0 ... ( 2 ) Find the solution of system of equation corresponding to r = 2 Substitute 2 for r in the system of equation: − 3 x 2 = 0 ... ( 3 ) x 1 − 4 x 2 = 0 ... ( 4 ) The value of x 1 = 0 and x 2 = 0 . Find the solution of system of equation corresponding to r = 1 Substitute 1 for r 1 in the system of equation: x 1 − 3 x 2 = 0

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 9.2, Problem 13E

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To prove: The system of equation 2x1−3x2=rx1, and x1−2x2=rx2 using the Gauss–Jordan elimination algorithm to has a unique solution for r1=2 but an infinite number of solutions for r1=1.

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Chapter 9.2, Problem 12E

Chapter 9.2, Problem 14E

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Fundamentals of Differential Equations and Boundary Value Problems

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To prove: The system of equation 2 x 1 − 3 x 2 = r x 1 , and x 1 − 2 x 2 = r x 2 using the Gauss–Jordan elimination algorithm to has a unique solution for r 1 = 2 but an infinite number of solutions for r 1 = 1 .

Solution Summary: The author analyzes the Gauss–Jordan elimination algorithm to prove that the system of equation rll2x_13X

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To prove: The system of equation 2x1−3x2=rx1, and x1−2x2=rx2 using the Gauss–Jordan elimination algorithm to has a unique solution for r1=2 but an infinite number of solutions for r1=1.

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