For a system of two linear differential equations, the only equilibrium point is (0,0). This is because the only solution vector that would make the coefficient matrix multiplied by the solution vector equal 0 is the zero vector due to the matrix being “invertible”. My question is, why does a matrix’s invertibility mean that only the zero vector can make the systems derivative equal zero?
For a system of two linear differential equations, the only equilibrium point is (0,0). This is because the only solution vector that would make the coefficient matrix multiplied by the solution vector equal 0 is the zero vector due to the matrix being “invertible”. My question is, why does a matrix’s invertibility mean that only the zero vector can make the systems derivative equal zero?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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For a system of two linear differential equations, the only equilibrium point is (0,0). This is because the only solution vector that would make the coefficient matrix multiplied by the solution vector equal 0 is the zero vector due to the matrix being “invertible”. My question is, why does a matrix’s invertibility mean that only the zero vector can make the systems derivative equal zero?
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