# Solving a system of equations

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Mitra Taghizadeh on 9 Aug 2022
Answered: Paul on 10 Aug 2022
Hello everyone.
I have a system of equations in matrix form like this: (This is just an example. In fact the size of matrix A is 13*1 and B is 13*53 and C is 53*13]).
A=B*C
A=[x1,y1,z1,0,0,0,1]'
B=[a1,a2,a3,0,0,0,a4;a5,a6,a7,0,0,0,0;a8,a9,a10,0,0,0,0;0,0,0,a11,a12,0,a13;0,0,0,a14,a15,0,a16;0,0,0,a17,a18,a19,a20;0,0,0,0,0,0,1];
C=[3,4,5,x2,y2,z2,1]'
In this equation x1,x2,y1,y2,z1,z2 are the unknowns and ai (i=1 to 20) are the known values.
Do you know how can I solve this system?
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Mitra Taghizadeh on 10 Aug 2022
Hi
Yes thank you.

Paul on 10 Aug 2022
Hi Mitra
Maybe this will extend to the larger problem.
syms x1 y1 z1 x2 y2 z2
syms a [1 20]
A=[x1,y1,z1,0,0,0,1].';
B=[a1,a2,a3,0,0,0,a4;a5,a6,a7,0,0,0,0;a8,a9,a10,0,0,0,0;0,0,0,a11,a12,0,a13;0,0,0,a14,a15,0,a16;0,0,0,a17,a18,a19,a20;0,0,0,0,0,0,1];
C=[3,4,5,x2,y2,z2,1].';
sol = solve(A==B*C,[x1 y1 z1 x2 y2 z2])
sol = struct with fields:
x1: 3*a1 + 4*a2 + 5*a3 + a4 y1: 3*a5 + 4*a6 + 5*a7 z1: 3*a8 + 4*a9 + 5*a10 x2: (a12*a16 - a13*a15)/(a11*a15 - a12*a14) y2: -(a11*a16 - a13*a14)/(a11*a15 - a12*a14) z2: (a11*a16*a18 - a12*a16*a17 - a13*a14*a18 + a13*a15*a17 - a11*a15*a20 + a12*a14*a20)/(a19*(a11*a15 - a12*a14))