## Linear ODEs in matrix form

Hi I have two linear coupled equations,

A'=-kA+mB
B'=-mB+kA

where A and B are dependant on time, and A' and B' are the derivatives of A and B with respect to time.

I know that the solution to these using eigenvalues and eigenvectors, can be found by using the equation.

x=c1 U1 exp(lambda1 *t) + c2 U2 exp(lambda2 *t)

where c1 and c2 are arbitrary constants. U1 and U2 are the eigenvectors and lambda1 and lambda2 are their corresponding eigenvalues. and x is the non-zero column vector [A' ; B']

I was wondering if anybody had a way of changing the above equation so that I could have it so that instead of the eigenvalues and eigenvectors being seperated they are together as a matrix of eigenvalues and a matrix of eigenvectors ???

I need it in this form for using in a MATLAB program, since my next task is with more equations (8 or more) and it would be easier if the formula was in a better form

Thanks