The discussion focuses on solving the system of differential equations represented by dx/dt = [12 -6; 6 -3] with the initial condition x(0) = [12; 9]. The key step involves finding the eigenvalues of the matrix [12 -6; 6 -3], which are λ = 3 and λ = -3. The correct formulation of the equation is emphasized as dx/dt = [12 -6; 6 -3]x. Participants clarify the process of deriving the eigenvalue equation, highlighting the importance of accurate calculations in this context.
PREREQUISITESStudents in mathematics or engineering, educators teaching linear algebra, and professionals working with systems of differential equations.
A assume you mean "dx/dt= [12 -6; 6 -3]x" or, in Latex,jrsweet said:Homework Statement
solve the system dx/dt = [12 -6; 6 -3] with the initial value x(0) = [12; 9]
That's wrong. Show us how you got the eigenvalue equation.Homework Equations
The Attempt at a Solution
I know I need to find the Eigenvalues but then I get a little confused from there.
(λ-3)(λ+3)=0
λ=3, -3