Consider the initial value problem {dy (t)dt=Ay(t) +φ(t), t≥0,y(0) = (0,0,···,0,0)T∈Rm−1,(0.1)where A=m2−2 11−2 1………1−2 11−2∈R(m−1)×(m−1),φ(t) =m2(1,0,···,0,−1)T∈Rm−1.(a) Find the all eigenvalues ofA.(b) Given m= 10ßsolve (0.1) by using Euler method with step- size h= 0.0045,0.01, respectively. Observe the numerical results att= 1 and present your comments.(c) Given m= 10ßsolve (0.1) by using implicit midpoint method with step sizeh= 0.0045,0.01, respectively. Compare with