The coefficient matrix A below is the sum of a nilpotent matrix and a multiple of the identity matrix. Use this fact to solve the given initial value problem. 1 45 4 x' = 0 1 4 x, x(0) = 5 001 8 Solve the initial value problem. x(t) = (Use integers or fractions for any numbers in the expression.)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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The coefficient matrix A below is the sum of a nilpotent matrix and a multiple of the identity matrix. Use this
fact to solve the given initial value problem.
1 4 5
4
x' =
0 1 4 x, x(0) = 5
001
8
Solve the initial value problem.
✓
x(t) =
(Use integers or fractions for any numbers in the expression.)
Transcribed Image Text:The coefficient matrix A below is the sum of a nilpotent matrix and a multiple of the identity matrix. Use this fact to solve the given initial value problem. 1 4 5 4 x' = 0 1 4 x, x(0) = 5 001 8 Solve the initial value problem. ✓ x(t) = (Use integers or fractions for any numbers in the expression.)
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