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12. Consider the linear homogeneous system x y = pu(t)x+ P12(t)y, P21(t)x+ P22(t)y. Show that if x = x₁(t), y = y₁(t) and x = x₂(t), y = y₂(t) are two solutions of the given system, then x = c₂x₁(t) + ₂x₂(t), y = c₁y₁(t) + c₂₂(t) is also a solution for any constants c, and c₂. This is the principle of superposition

12. Consider the linear homogeneous system x y = pu(t)x+ P12(t)y, P21(t)x+ P22(t)y. Show that if x = x₁(t), y = y₁(t) and x = x₂(t), y = y₂(t) are two solutions of the given system, then x = c₂x₁(t) + ₂x₂(t), y = c₁y₁(t) + c₂₂(t) is also a solution for any constants c, and c₂. This is the principle of superposition

Elementary Linear Algebra (MindTap Course List)
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 90E: Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the...
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12. Consider the linear homogeneous system XI y! P₁1(t)x+ P12(t)y, P21 (t)x+ P22 (t)y. Show that if x= x₁(t), y = y₁(t) and x= x₂(t), y = y₂(t) are two solutions of the given system, then x = ₁x₁(t) + ₂x₂(t), y = c₁y₁(t) + ₂y₂(t) is also a solution for any constants c₁ and c₂. This is the principle of superposition
Transcribed Image Text:12. Consider the linear homogeneous system XI y! P₁1(t)x+ P12(t)y, P21 (t)x+ P22 (t)y. Show that if x= x₁(t), y = y₁(t) and x= x₂(t), y = y₂(t) are two solutions of the given system, then x = ₁x₁(t) + ₂x₂(t), y = c₁y₁(t) + ₂y₂(t) is also a solution for any constants c₁ and c₂. This is the principle of superposition
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