irst verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they olution of the system. 13 -4 4e 6t 3t x; X = .X2 = 4 e 28 - 10 3t 13 -4 13 -4 4e 6t 6t 24 e 28 - 10 28 - 10 7e 6t 42 e 6t 13 -4 13 -4 - 3t X2 = 28 - 10 28 - 10 - 3t 4 e

irst verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they olution of the system. 13 -4 4e 6t 3t x; X = .X2 = 4 e 28 - 10 3t 13 -4 13 -4 4e 6t 6t 24 e 28 - 10 28 - 10 7e 6t 42 e 6t 13 -4 13 -4 - 3t X2 = 28 - 10 28 - 10 - 3t 4 e

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.5: Iterative Methods For Solving Linear Systems

Problem 5EQ

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Question

First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general
solution of the system.
13
x' =
-4
x; x, =
4 e 6t
e -3
X2 =
icori
28 - 10
Ze 6t
4e -3t
13
- 4
13
- 4
4 e 6t
24 e 6t
x, 3D
=x,'
28 - 10
28 - 10
7e 6t
42 e 6t
13
- 4
13
- 4
- 3t
e
28 - 10
28 - 10
4e -3t
3, 4e

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