Question

anyone know about differential equations? like if I have a matrix times x, can I just use A-Iλ=0 to get the general solution?

Answer 1

det(A- lambda I) WILL GIVE U EIGENVALUES

Answer 2

Essentially right now your have a set of linear equations in the form x' =Ax. To the values of the functions x you use eigenvalues and eigenvectors. Using the det(A-Iλ)=o will give you eignvaluess of which you plug back into the matrix to solve for the eigen vectors.

Your solution will be in the form

x = c1x(t)1 + c2x(t)2 + cnx(t)n

Answer 3

Where the constant values cn will be your eigenvectors and x(t) will be the exponential function namely of e^λt where lambda is the corresponding eigenvalue.

Answer 4

Is this what your were asking?