In python find matrix M
I have the matrix X
X=[5.8 3.0 3.7 1.9]
and need to create a matrix M that is 4x150 that has the the
values of matrix X inside it for every row
M=
5.8
3.0
3.7
1.9
5.8
3.0
3.7
1.9
5.8
3.0
3.7
1.9
5.8
3.0
3.7
1.9
5.8
3.0
3.7
ect
5.8
ect
ect
5.8
ect
5.8
1a.) find the eigenvalues of x"+(lambda)(x) = 0, x(0)=x'(pi)=0
1b.) Solve ut=((c)^2)u(xx) , u(0,x)= alpha * sin x, with the boundary condition u(t,0)=u(t,pi)=0
1c.) Solve ut = u(xx), u(0,x) = alpha * sin ((pi*x)/(L)), with the boundary condition u(t,0) = u(t,L) = 0.
(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.
Consider the boundary value problem X ′′ +λX=0 , X ′ (0)=0 ,
X′(π)=0 . Find all real values of λ for which there is a
non-trivial solution of the problem and find the corresponding
solution.
Consider a system of N particles in an infinite
square well fro, x=0 to x=N*a.
find the ground state wave function and
ground state energy for
A. fermions.
B. bosons.
. We have the following algorithm.
Algorithm Novel(X[0..m-1, 0..m-1])
//Input: A matrix X[0..m-1, 0..m-1] of real numbers
for i←0 to m-2 do
for j←i+1 to m-1 do
if X[i,j] ≠X[j, i]
return false
return true
a. What does this algorithm compute?
b. What is its basic operation?
c. How many times is the basic operation executed?
d. What is the efficiency class of this algorithm?