Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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5. Given a square matrix A and two eigenpairs (λ, x.), i = 1, 2, with λǐメλ2, prove that the eigenvectors {x1,T2} form a linearly independent set. Hint: let 1, 2 and apply A to both sides of (1), for two scalars ci, C2, note that Ax,-Azi, and prove that C1 C2 。
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Transcribed Image Text:5. Given a square matrix A and two eigenpairs (λ, x.), i = 1, 2, with λǐメλ2, prove that the eigenvectors {x1,T2} form a linearly independent set. Hint: let 1, 2 and apply A to both sides of (1), for two scalars ci, C2, note that Ax,-Azi, and prove that C1 C2 。
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