Problem 7: For the following matrix A, use diagonalization to find A" for any given positive integer n. A=(-¹) 4
Problem 7: For the following matrix A, use diagonalization to find A" for any given positive integer n. A=(-¹) 4
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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Transcribed Image Text:Problem 7: For the following matrix A, use diagonalization to find A" for any given
positive integer n.
(
(Hint: If A = PDP-¹, then show by induction on n that A” = PD™ P−¹.)
A
=
Expert Solution
Step 1 Find the eigen values of A
A=
Trace of A = 6 + -1 = 5
Determinant of A = -6 +12 = 6
Sum of eigen values of A = Trace(A)=5
Product of eigen values of A = Det(A)= 6
The two numbers whose sum and product are 5 and 6 are 3 and 2. Thus the two eigen values of A are 2 and 3
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