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Get Full Access to Numerical Analysis - 10 Edition - Chapter 4.1 - Problem 1
Get Full Access to Numerical Analysis - 10 Edition - Chapter 4.1 - Problem 1

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# Solved: Use the forward-difference formulas and backward-difference formulas to ISBN: 9781305253667 457

## Solution for problem 1 Chapter 4.1

Numerical Analysis | 10th Edition

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Problem 1

Use the forward-difference formulas and backward-difference formulas to determine each missing entry in the following tables, a. X fix) fix) b. X fix) fix) 0.5 0.4794 0.0 0.00000 0.6 0.5646 0.2 0.74140 0.7 0.6442 0.4 1.3718

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Section 4.1 Eigenvalues and Eigenvectors Definition: Let A be an n ×n matrix, u be a nonzero n ×1 vector, and λ be a constant. If Au = λu then λ is called an eigenvalue for the matrix A and u is called the eigenvector corresponding to λ . Example: Let 35 −10 A =   and u =  1 −1   −2  Find the eigenvalue, , corresponding to the eigenvector, u. Solution: Au = λu so 5 −10  −10   = λ    −1 −  −2  −40  −10    = λ   −8   −2  λ = 4 λ Theorem: is an eigenvalue for A if and only ifA) − λI is not invertible. R

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##### ISBN: 9781305253667

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