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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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