Dear all;
I need your help to solve the non-square system of equation
restart;
with(LinearAlgebra);
l1 := [1, 1, 1, 0, 0, 0, 0, 0, 0];
l2 := [0, 0, 0, 1, 1, 1, 0, 0, 0];
l3 := [0, 0, 0, 0, 0, 0, 1, 1, 1];
l4 := [1, 0, 0, 1, 0, 0, 1, 0, 0];
l5 := [0, 1, 0, 0, 1, 0, 0, 1, 0];
l6 := [0, 0, 1, 0, 0, 1, 0, 0, 1];
l7 := [0, 0, 1, 0, 1, 0, 1, 0, 0];
A := Matrix([l1, l2, l3, l4, l5, l6, l7]);
# Unknown vector
m := [m1, m2, m3, m4, m5, m6, m7, m8, m9];
# Right hand side
b = [15, 15, 15, 15, 15, 15, 15];
# Let the matrix equation : A m =b
1)I need your help to compute the kernel and general solution of this matrix equation
2) can we find a solution if m_k in { 2 3 4 5 6 7 8 } and each of these number appears at least once
3) If there a solution if we consider m_k in the set {0 1 2 3 4 5 6 7 8 } and the number used exactly one
Thank you very much for your help