Matrix System

Please solve the attached system (give solution in real form)

Equivalent Systems

Write the given second order equation as its equivalent system of first order equations {see attachment} Use v to represent the "velocity function" Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) Now write the system using matrices {see attachment}. The initial value for the vector valued function is ... ?

eigenvalues

Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues..... (see attached)

solving system

Solve the system with the initial value... see attached

solve system

Solve the system attached - Give your solution in real form.