Homogeneous EquationsThe homogeneous matrix equation involves a zero right-hand side. This equation has a nonzero solution if the matrix is singular. To test if a matrix is singular, you can compute the determinant. In[1]:=  |
Out[2]=
|
To find the solution of the homogeneous equation you can use the function NullSpace. This returns a set of orthogonal vectors, each of which solves the homogeneous equation. In the example below, there is only one vector. In[3]:=  |
Out[3]=
|
This demonstrates that the solution in fact solves the homogeneous equation. In[4]:=  |
Out[4]=
|
The function Chop can be used to replace approximate numbers close to 0. In[5]:=  |
Out[5]=
|
The solution to the homogeneous equation can be used to form an infinite number of solutions to the inhomogeneous equation. This solves an inhomogeneous equation. In[6]:=  |
Out[7]=
|
The solution does in fact solve the equation. In[8]:=  |
Out[8]=
|
If you add to sol an arbitrary factor times the homogeneous solution, this new vector also solves the matrix equation. In[9]:=  |
Out[9]=
|
| 
