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Let A be an n x n matrix with characteristic polynomial f(1) = (-1)*t" + a,-1t"-1 +... + a,t + ao. Prove that f(0) = a, = det(A). Deduce that A is invertible if and only if 40 + 0. %3D

Let A be an n x n matrix with characteristic polynomial f(1) = (-1)*t" + a,-1t"-1 +... + a,t + ao. Prove that f(0) = a, = det(A). Deduce that A is invertible if and only if 40 + 0. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let A be an n x n matrix with characteristic polynomial f(1) = (-1)*t" + a,-1t"-1 +... + a,t + ao. Prove that f(0) = a, = det(A). Deduce that A is invertible if and only if 40 + 0. %3D
Transcribed Image Text:Let A be an n x n matrix with characteristic polynomial f(1) = (-1)*t" + a,-1t"-1 +... + a,t + ao. Prove that f(0) = a, = det(A). Deduce that A is invertible if and only if 40 + 0. %3D
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