Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 12E
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Question
Find general solutions of the systems in Problem Attached.
Expert Solution
Step 1
Consider the given system of equations
Compare the given system of differential equation with x' = Ax
The matrix A is an upper diagonal matrix.
The eigenvalues of upper diagonal matrix are diagonal elements.
The eigenvalues of matrix A are 2, 2, 2, 2.
That is an eigenvalue of A is 2 with algebraic multiplicity 4.
Step 2
Consider,
Hence, λ = 2 is eigenvalue with algebraic multiplicity 4 and defect 3.
Therefore, any non-zero vector v4 is the solution of (A - 2I)4v4 = 0.
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