Explanation Definition used: Derivative of a matrix of functions: If X ( t ) = ( a i j ( t ) ) m × n is a matrix whose entries are functions differentiable on a common interval, then d X d t = [ d d t a i j ] m × n . Calculation: The given matrix X ( t ) is [ 1 2 sin 2 t − 4 cos 2 t − 3 sin 2 t + 5 cos 2 t ] . Use the above mentioned definition to obtain the derivative of the given matrix as follows

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter B, Problem 26E

To determine

The value of dXdt for the matrix X = [12sin2t−4cos2t−3sin2t+5cos2t].

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Chapter B Solutions

Differential Equations with Boundary-Value Problems (MindTap Course List)

Ch. B - Prob. 1E Ch. B - Prob. 2E Ch. B - Prob. 3E Ch. B - Prob. 4E Ch. B - Prob. 5E Ch. B - Prob. 6E Ch. B - Prob. 7E Ch. B - Prob. 8E Ch. B - Prob. 9E Ch. B - Prob. 10E

Ch. B - Prob. 11E Ch. B - Prob. 12E Ch. B - Prob. 13E Ch. B - Prob. 14E Ch. B - In Problems 1522 determine whether the given...Ch. B - Prob. 16E Ch. B - Prob. 17E Ch. B - Prob. 18E Ch. B - Prob. 19E Ch. B - Prob. 20E Ch. B - Prob. 21E Ch. B - In Problems 1522 determine whether the given...Ch. B - Prob. 23E Ch. B - Prob. 24E Ch. B - Prob. 25E Ch. B - Prob. 26E Ch. B - Prob. 27E Ch. B - Prob. 28E Ch. B - Prob. 29E Ch. B - Prob. 30E Ch. B - Prob. 31E Ch. B - Prob. 32E Ch. B - Prob. 33E Ch. B - Prob. 34E Ch. B - Prob. 35E Ch. B - Prob. 36E Ch. B - Prob. 37E Ch. B - Prob. 38E Ch. B - Prob. 39E Ch. B - Prob. 40E Ch. B - Prob. 41E Ch. B - Prob. 42E Ch. B - Prob. 43E Ch. B - Prob. 44E Ch. B - Prob. 45E Ch. B - Prob. 46E Ch. B - Prob. 47E Ch. B - Prob. 48E Ch. B - Prob. 49E Ch. B - Prob. 50E Ch. B - Prob. 51E Ch. B - Prob. 52E Ch. B - Prob. 53E Ch. B - Prob. 54E Ch. B - Prob. 55E Ch. B - Prob. 56E Ch. B - Prob. 57E Ch. B - Prob. 58E Ch. B - Prob. 59E Ch. B - Prob. 60E Ch. B - Prob. 61E Ch. B - Prob. 62E

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The value of d X d t for the matrix X = [ 1 2 sin 2 t − 4 cos 2 t − 3 sin 2 t + 5 cos 2 t ] .

Solution Summary: The author calculates the derivative of the given matrix with respect to t by using the above-mentioned definition.

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The value of dXdt for the matrix X = [12sin2t−4cos2t−3sin2t+5cos2t].

Chapter B Solutions