Finding a variable value using no fzero etc.

Hi I have another problem that I cannot using fzero or solve or any method that uses initial answers because It can produce the exact answer

Y(t,j)=[0,0,1,0;1,0,0,0;0,0,0,1;0,1,0,0];

A(i,j)=[1,4,6,2;4,5,2,3;5,3,2,4];

now I have K(i,j) which needs to be calculated as follow

sigma(Y(1,j)*(K(1,j)-A(1,j)))=0

this part is simple I could easily calculate K(1,j) after having K(1,j) I need to use it in the following equation to calculate K(t,j)

sigma( sigma(Y(t,j)*(K(1,j)-(sigma(Y(t-1,f)*K(1,f)+A(1,j)))))=0

I calculated the answer K(1,3) = 6 from equation 1

from equation 2 we have K(1,1)=7, K(1,4)=9, K(1,2)=13

it can be easily calculated because it is gradually like this Y(K-A)=0 and we have y that is one and A

The problem is : how can I code the second equation that I would be able to calculate K(t,j) and use it in another equation? no fzero, solve etc. can anyone help?

[Matt J]

because It can produce the exact answer

Do you mean "can", or did you really mean "can't"? No solver will produce an exact answer. You always have inexact calculations in finite precision computers.

Answer 1

[Matt J]

Your equations are linear, so you just have to build an appropriate matrix equation

P*X=Q

and solve as X=P\Q

[alexaa1989]

yeah thanks that occurred to me too. It is related to linear numerical algebra or something like that but HOW?

[Matt J]

You have equations of the form

 sigma_j Pij *Kj = Qi

This is equivalent to

P*K=Q

where Pij are the entries of the matrix P and Qi are the entries of the vector Q.

[alexaa1989]

that works for first equation second one is much more complicated for me I couldnt write it

[Matt J]

There shouldn't be a fundamental difference. Both summations are equivalent to weighted sums of the K(i) with different sets of coefficients. Just put the coefficients into the rows of a matrix, one row per equation.

[alexaa1989]

the second summation have another K(1,f) in it

that makes everything different I have been trying to code it for a week now