MATLAB Solving equations problem

Question

I want to solve these equations using MATLAB and I am sure there is a non zero solution. The equations are:

0.7071*x            + 0.7071*z = x 
  -0.5*x +         


        

Answer 1

I don't think you need to use the solve function as your equations is a system of linear equations.

Recast as a matrix equation:

Ax = B

In your case:

    | -0.2929   0.0      0.7071  |  | x |     | 0 |
    | -0.5     -0.2929   0.5     |  | y |  =  | 0 |
    | -0.5     -0.7071  -0.5     |  | z |     | 0 |

Use the built-in functionally of MATLAB to solve it. See e.g. MATLAB: Solution of Linear Systems of Equations.

The core of MATLAB is to solve this kind of equation.

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Using FreeMat (an open-source MATLAB-like environment with a GPL license; direct download URL for Windows installer):

   A = [ -0.2929 0.0 0.7071; -0.5 -0.2929 0.5; -0.5 -0.7071 -0.5 ]

   B = [0.0; 0.0; 0.0]

   A\B

   ans =
    0
    0
    0

So the solution is: x = 0, y = 0, z = 0

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The solution can also be derived by hand. Starting from the last two equations:

    -0.5*x + 0.7071*y +    0.5*z = y
    -0.5*x - 0.7071*y +    0.5*z = z

    0.2929*y =  -0.5*x + 0.5*z
    0.7071*y =  -0.5*x + 0.5*z

    0.2929*y = 0.7071*y

Thus y = 0.0 and:

    0.7071*y =  -0.5*x + 0.5*z

    0 =  -0.5*x + 0.5*z

    0 =  -0.5*x + 0.5*z

    0.5*x = 0.5*z

    x = z

Inserting in the first equation:

    0.7071*x + 0.7071*z = x 

    0.7071*x + 0.7071*x = x 

    1.4142*x = x 

Thus x = 0.0. And as x = z, then z = 0.0.