Solving Linear System of Equations with a Real Parameter

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

[darova]

What do you know about mathematics?

What can you say about this:

[Star Strider]

@Gauss — Our apologies.

[Gauss]

You are not the problem, disrespectful people are.

Every time I ask on a forum looking for help I get insulted.

Not the right way to behave, for sure.

If you know the answer to mi question though I'd appreciate it.

Thanks

[Star Strider]

@Gauss —

My pleasure.

Jim Riggs posted one that may be helpful.

Answer 1

[Jim Riggs]

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]

Thanks a lot ;)

Answer 2

[Steven Lord]

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.