Further Examples: NullSpace

Here is a nonsingular matrix.

In[1]:=

Out[1]=

That is, the null space of the nonsingular matrix mm is trivial. There is no nonzero vector v such that mm.v = 0.

In[2]:=

Out[2]=

Here the null space has dimension .

In[3]:=

Out[3]=

This checks the result.

In[4]:=

Out[4]=

These two vectors span the null space of the matrix m2x4.

In[5]:=

Out[5]=

Multiplying m2x4 by any linear combination of the vectors v1 and v2 gives the zero vector.

In[6]:=

Out[6]=

This simplifies the expression.

In[7]:=

Out[7]=

The rank of the matrix is the difference between the dimension of the range and the dimension of the null space.

In[8]:=

Out[8]=

In[9]:=