Suppose that A is square matrix, prove that: • the sum of its eigenvalues is equal to the trace of A; • the product of its eigenvalues is equal to the determinant of A.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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Suppose that A is square matrix, prove that:
• the sum of its eigenvalues is equal to the trace of A;
• the product of its eigenvalues is equal to the determinant of A.
Transcribed Image Text:Suppose that A is square matrix, prove that: • the sum of its eigenvalues is equal to the trace of A; • the product of its eigenvalues is equal to the determinant of A.
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