# Solving Linear System of Equations with a Real Parameter

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Gauss on 30 Nov 2019
Answered: Steven Lord on 2 Dec 2019
Hi, I'm a University Student, I never used Matlab and I have to solve with Matlab several Linear Systems of Equations with a Real Parameter, like this: λ∈ℝ
Since I really don't know anything about Matlab it would be great if there is some sort of Pre-Compiled code to solve this kind of Systems so every time I just have to replace the values in the equations and I can easily get the solutions I need.
Thanks a lot,
Have a nice one
Star Strider on 30 Nov 2019
@Gauss —
My pleasure.
Jim Riggs posted one that may be helpful.

Jim Riggs on 30 Nov 2019
Edited: Jim Riggs on 30 Nov 2019
Using the symbolic toolbox, you can solve it as follows:
1) Define symbolic quantities;
syms A B x1 x2 x3 x4 lamda
2) Write the problem in matrix form
A = [1 0 1 0; lamda 1 0 1; 1 1 1 1; 2 1 lamda 0; 0 0 1 1]; % 5 x 4 coefficient matrix
B = [x1; x2; x3; x4] % 4 x 1 column matrix
3) solve the system of equations
[v1, v2, v3, v4, v5] = solve(A*B==[1; lamda; 1; lamda; 1]);
The result:
v1 = value of x1
v2 = value of x2
v3 = value of x3
v4 = value of x4 and
v5 = value of lamda
I get two sets of solutions:
v1 v2 v3 v4 v5 = 0 0 1 0 0 and
v1 v2 v3 v4 v5 = 1 1 -1 0 1
Gauss on 30 Nov 2019
Thanks a lot ;)

Steven Lord on 2 Dec 2019
What do you know and what are you trying to find?
Do you know the value of λand you're trying to find the X values? If so, build your coefficient matrix and right-hand side vector and use the backslash operator (\) to solve the system. Both the coefficient matrix and right-hand side will include λ. See the documentation page for the mldivide function for more information.
Do you know the values of X and you're trying to find λ? If so, you could use fzero on one of the equations that involve λ.
Do you know neither λ nor the values of X and you're trying to find all five? In this case you don't have a linear system, you have a nonlinear system (due to the λ*X1 and λ*X3 terms) and so you'd need to use something like fsolve from Optimization Toolbox.