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det (AI - A) = T n + k=0 where oo (A1,..., An) = 1, and, for 1 ≤ k ≤n, Ok (A1,..., An) = ✦✦ (-1)* ok (₁, ..., An) X™—*, n-k D | A | [T | Σ Aj₁Ajk. <…..

det (AI - A) = T n + k=0 where oo (A1,..., An) = 1, and, for 1 ≤ k ≤n, Ok (A1,..., An) = ✦✦ (-1)* ok (₁, ..., An) X™—*, n-k D | A | [T | Σ Aj₁Ajk. <…..

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 11E
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det (AI - A) = n + Q (-1) σk (A₁,..., An) A¹-k, k=0 where oo (A₁,..., An) = 1, and, for 1 ≤ k ≤n, σκ(λι,...,λη) = Σ O | D | AV Aj₁Ajk 1<ji<--<jk ≤n The polynomials o are called the elementary symmetric polynomials. 8. If A, B € M(n, C), B invertible, and D = B-¹AB, show that, for all kEN, D = B-¹AK B. A100 9. Let A denote the first matrix in Exercise 2. Diagonalize A and use this to compute
Transcribed Image Text:det (AI - A) = n + Q (-1) σk (A₁,..., An) A¹-k, k=0 where oo (A₁,..., An) = 1, and, for 1 ≤ k ≤n, σκ(λι,...,λη) = Σ O | D | AV Aj₁Ajk 1<ji<--<jk ≤n The polynomials o are called the elementary symmetric polynomials. 8. If A, B € M(n, C), B invertible, and D = B-¹AB, show that, for all kEN, D = B-¹AK B. A100 9. Let A denote the first matrix in Exercise 2. Diagonalize A and use this to compute
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