Find the eigenvalues and eigenfunctions of the Sturm-Liouville
system
y"+ lamda y = 0 o<x<1
y(0) = 0
y'(1) = 0
(b) Show that the eigenfunctions Yn and Ym you obtained from the
above
are orthogonal if n not= m.
(a) Find a 3×3 matrix A such that 0 is the only eigenvalue of A,
and the space of eigenvectors of 0 has dimension 1. (Hint: upper
triangular matrices are your friend!)
(b) Find the general solution to x' = Ax.
PLEASE SHOW YOUR WORK CLEARLY.
Find the absolute max and min of f(x)= e^-x sin(x) on the
interval [0, 2pi]
Find the absolute max and min of f(x)= (x^2) / (x^3 +1) when x
is greater or equal to 0