Explanation Let A ( t ) = [ 1 1 0 0 ] . Then, det ( A ) = 0 . Consider the vector differential equation x ′ ( t ) = A ( t ) x ( t ) [ x 1 ′ x 2 ′ ] = [ 1 1 0 0 ] [ x 1 x 2 ] Observe that [ e t − 1 1 ] , [ e t − 2 2 ] are two solutions of the above system.

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Question

Chapter 9.2, Problem 5TFR

To determine

Whether the statement, “If A is a 2×2 matrix of constants whose determinant is zero, then the vector differential equation x′(t)=Ax(t) cannot have two linearly independent solutions” is true or false.

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Chapter 9.2, Problem 4TFR

Chapter 9.2, Problem 6TFR

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Chapter 9 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 5TFR Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 7TFR Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 9TFR Ch. 9.1 - Prob. 10TFR

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Whether the statement, “If A is a 2 × 2 matrix of constants whose determinant is zero, then the vector differential equation x ′ ( t ) = A x ( t ) cannot have two linearly independent solutions” is true or false.

Solution Summary: The author analyzes whether the statement, "If A is a 2times 2 matrix of constants whose determinant is zero, then the vector differential equation xprime

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Whether the statement, “If A is a 2×2 matrix of constants whose determinant is zero, then the vector differential equation x′(t)=Ax(t) cannot have two linearly independent solutions” is true or false.

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Chapter 9 Solutions