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Question: Sovle a differential equation of matrix S given a matrix filled with variables

Question:Sovle a differential equation of matrix S given a matrix filled with variables

pooh 4 Maple
February 21 2009
0

F:= <<-3u|u|u|u>, <u|-3u|u|u>, <u|u|-3u|u>,<u|u|u|-3u>>;

S := Matrix(4,4,(i,j) -> s[i,j](t));



Given the properties that S_1,1(t) + S_1,2(t)+ S_1,3(t) + S_1,4(t) =1

                          S_2,1(t) + S_2,2(t)+ S_2,3(t) + S_2,4(t) =1
                          S_3,1(t) + S_3,2(t)+ S_3,3(t) + S_3,4(t) =1
                          S_4,1(t) + S_4,2(t)+ S_4,3(t) + S_4,4(t) =1

                          S_i,i(0) = 1
                          S_i,j(0) = 0

The matrix equation:
dS/dt=SF

Can we find matrix S where each element is in term of ut?

thanks.
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