The formula in Problem 29 can be used to compute A 2 without an explicit matrix multiplication.

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The formula in Problem 29 can be used to compute A² without an explicit matrix multiplication. It follows that

without an explicit matrix multiplication

and so on. Use this method to compute A², A³, A⁴, and A⁵ given

Problems 28 through 30 develop a method of computing powers of a square matrix.

Problem 29

where I denotes the 2 x 2 identity matrix. Thus every 2 x 2 matrix A satisfies the equation

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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Question Posted: Jul 06, 2023 09:27 AM

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The formula in Problem 29 can be used to compute A 2 without an explicit matrix multiplication.

Question:

3 A³ = (a + d)A² - (ad - bc)A

Step by Step Answer:

If A 2 1 12 A 4A31 4 A 4A3A A 4A3A then ad ...View the full answer

Differential Equations And Linear Algebra

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