Consider the matrix
a=(1 1 2
1 2 -1
3 2 1
5 5 2)
Find N(A), R(A), N(A^T),R(A^T). Show that the fundamental subspace theorem holds: N(A^T)=R(A)^(upside down T), N(A)=R(A^T)^(upsidedown T).
Hint: Notice that the fourth row is the sum of the first three rows.
This gives a matrix and then proves that the fundamental subspace theorem holds.