Verify that X t is a fundamental matrix for the given system

Last updated: 8/3/2023

Verify that X t is a fundamental matrix for the given system and compute X t Then use the result that if X t is a fundamental matrix for the system x Ax then x t X t x 0 x is the solution to the in alue problem x Ax x 0 xo 060 x 1 0 1 X 1 1 0 x 0 X Ax X AX2 X3 AX3 2 0 5 X t 24e 6e 2t 4e t 20e t 6e t 2e 2t 3e t 2e 2t 3e t C 060 a If X t x t x t X3 t and A 1 0 1 validate the following identities and write the column vector that equals each side of the equation 110 b Next compute the Wronskian of X t W X1 t x t X3 t Since the Wronskian is never r and each column of X t is a solution to x Ax X t is a fundamental matrix