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Problem 3. (a) (b) (c) Let A be an n x n matrix with characteristic polynomial: +an-2 +...+ a₁t+ao f(t) = (-1)" " + an-1t"-1 Which terms of f(t) represent det(4)? If A is invertible, prove that A¹ = (-1/a₂)[(-1)" 4"-¹ +an-1-4-²+A₁-2t¹-¹ +...+₁₂] 12 1 3 Calculate A¹ for A = 0 2 00-1 by using (b).

Problem 3. (a) (b) (c) Let A be an n x n matrix with characteristic polynomial: +an-2 +...+ a₁t+ao f(t) = (-1)" " + an-1t"-1 Which terms of f(t) represent det(4)? If A is invertible, prove that A¹ = (-1/a₂)[(-1)" 4"-¹ +an-1-4-²+A₁-2t¹-¹ +...+₁₂] 12 1 3 Calculate A¹ for A = 0 2 00-1 by using (b).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3. (a) e (c) Let A be an n x n matrix with characteristic polynomial: f(t) = (-1)"t" + a₁-₁t"-1 + a₂-2t"-1. ++at+ao Which terms of f(t) represent det(4)? If A is invertible, prove that A¹ = (-1/a₁)[(-1)" A"-¹ + a₂-₁A¹-² + a₁_₂t¹−¹ + ... + a₁Ï„] 1 3 0 0 -1 1 2 Calculate A¹ for A 0 2 by using (b).
Transcribed Image Text:Problem 3. (a) e (c) Let A be an n x n matrix with characteristic polynomial: f(t) = (-1)"t" + a₁-₁t"-1 + a₂-2t"-1. ++at+ao Which terms of f(t) represent det(4)? If A is invertible, prove that A¹ = (-1/a₁)[(-1)" A"-¹ + a₂-₁A¹-² + a₁_₂t¹−¹ + ... + a₁Ï„] 1 3 0 0 -1 1 2 Calculate A¹ for A 0 2 by using (b).
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