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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald
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Show that the signals in Exercises 3–6 form a basis for

Chapter 4, Problem 3E

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QUESTION:

Show that the signals in Exercises 3–6 form a basis for the solution set of the accompanying difference equation.The signals and equation in Exercise 1Reference:Verify that the signals in Exercises 1 and 2 are solutions of the accompanying difference equation.

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QUESTION:

Show that the signals in Exercises 3–6 form a basis for the solution set of the accompanying difference equation.The signals and equation in Exercise 1Reference:Verify that the signals in Exercises 1 and 2 are solutions of the accompanying difference equation.

ANSWER:

Solution 3EStep 1 of 3Consider the signals and the difference equation .Th object of the problem is to show that the given signals form a basis for the solution of the difference equation.Verify the set of signals is linearly independent.For any scalars , , where are any scalars.Write this in matrix notation as This is a homogeneous system.Take the coefficient matrix called as Casorati matrix of the signals .

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