Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³ and 2 = ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det | These solutions are linearly independent because the Wronskian is Choose for all x.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...
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,3x
Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³x
and ze
ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the
solutions are linearly independent.
Wronskian = det
TE
These solutions are linearly independent because the Wronskian is
Choose
✓for all x.
Transcribed Image Text:,3x Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³x and ze ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det TE These solutions are linearly independent because the Wronskian is Choose ✓for all x.
Use the Wronskian to determine whether the functions y₁
=
Wronskian = det
[
sin(2x) and y2 = cos(6x) are linearly independent.
]
=
These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of x.
Transcribed Image Text:Use the Wronskian to determine whether the functions y₁ = Wronskian = det [ sin(2x) and y2 = cos(6x) are linearly independent. ] = These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of x.
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