Consider the matrices 4-17] ¹=[₁₂7], B = [1 2] ₁ A 5-7] [2] = i) Find A¹0 times vector b by writing vector bas linear combination of eigen vectors of A ii) Find a formula for AK for all non-negative integers k. (Can k be a negative integer?) iii) Use (ii) to find A¹0 times vector band compare it with what you found in (i).

Consider the matrices 4-17] ¹=[₁₂7], B = [1 2] ₁ A 5-7] [2] = i) Find A¹0 times vector b by writing vector bas linear combination of eigen vectors of A ii) Find a formula for AK for all non-negative integers k. (Can k be a negative integer?) iii) Use (ii) to find A¹0 times vector band compare it with what you found in (i).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

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