FindE₁ =Consider the following Gauss-Jordan reduction:020E₂ =Write A as a product A = Е₁ ¹₂ ¹Е ¹¹ of elementary matrices:-50100⠀⠀⠀⠀⠀1 -2 0 → 1 -2 0 ➜ 1 0 00 01E₂E₁A0 2 -50 0 10 20 0 1E₁ AE31 0 00 2 0 → 0 10 0 1E₂E₂E₁A0000 01E₁E₁ E₂E₂E, A= I

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Find E₁ = 0 1 Consider the following Gauss-Jordan reduction: 2 -5 -2 0 0 1 E₂ = 0 2 ⠀⠀⠀⠀⠀ 1 -2 0 → 1 0 0 00 1 E₂E, A 0 2 -5 Write A as a product A = E₁¹E ¹E, ¹E ¹ of elementary matrices: 1 -2 0 0 0 1 0 2 0 0 0 1 E₁A E3 = 1 0 0 0 0 1 10 0 2 0 →→ 0 10 E₂E₂E, A 07 0 0 1 E₁E₂E₂E, A E₁ = = I

Find E₁ = 0 1 Consider the following Gauss-Jordan reduction: 2 -5 -2 0 0 1 E₂ = 0 2 ⠀⠀⠀⠀⠀ 1 -2 0 → 1 0 0 00 1 E₂E, A 0 2 -5 Write A as a product A = E₁¹E ¹E, ¹E ¹ of elementary matrices: 1 -2 0 0 0 1 0 2 0 0 0 1 E₁A E3 = 1 0 0 0 0 1 10 0 2 0 →→ 0 10 E₂E₂E, A 07 0 0 1 E₁E₂E₂E, A E₁ = = I

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 50EQ

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