Lay Chapter 4,

Vector Spaces

dim(domain) == dim(kernel) + dim(range)

Consider a certain 3x4 matrix.

In[1]:=

The matrix a can be interpreted as the matrix of a linear map,

and the dimensions of certain vector spaces associated with that linear map will satisfy a well-known relationship.

In[2]:=

Out[2]=

Let's write some procedures which will make that relationship more transparent.

In[3]:=

Test those procedures on the matrix a.

In[6]:=

Out[6]=

Out[7]=

Out[8]=

Out[9]=

Basis for the Kernel of a Linear Map

Consider a certain 2x4 matrix.

In[20]:=

The matrix a can be interpreted as the matrix of a linear map,

We seek a basis for the null space of this linear map.

In[22]:=

Out[23]//MatrixForm=

Created by Mathematica (December 12, 2004) |