Explanation Given: The matrix is x ( t ) = [ e 2 t e 3 t − e 2 t − 2 e 3 t ] . Approach: A matrix is a rectangular array of numbers arranged in rows and columns where the element in the i th row and j th column is a i j . A ( t ) is differentiable at t 0 if each entry a i j ( t ) is differentiable at t 0 , and we write d A d t ( t 0 ) = A ′ ( t 0 ) : = [ a ′ i j ( t 0 ) ] . Calculation: Considering given equation First take RHS = [ 1 − 1 2 4 ] [ e 2 t e 3 t

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Chapter 9.3, Problem 37E

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To verify:

The system x′=[1−124]x.

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Chapter 9.3, Problem 36E

Chapter 9.3, Problem 38E

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To verify: The system x ′ = [ 1 − 1 2 4 ] x .

Solution Summary: The author explains how the matrix is a rectangular array of numbers arranged in rows and columns.

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To verify:

The system x′=[1−124]x.

Want to see the full answer?

Chapter 9 Solutions

To verify: The system x ′ = [ 1 − 1 2 4 ] x .

Solution Summary: The author explains how the matrix is a rectangular array of numbers arranged in rows and columns.

Concept explainers

Videos

To verify: The system x′=[1−124]x.

Want to see the full answer?

Chapter 9 Solutions

To verify:

The system x′=[1−124]x.