EXAMPLE 2 Recall that the null space of the matrix A in Example 6 in Section 2 had a basis of 3 vectors. So the dimension of Nul A in this case is 3. Observe how ea
basis vector corresponds to a free variable in the equation Ax = 0. Our constructi
always produces a basis in this way. So, to find the dimension of Nul A, simply identi
and count the number of free variables in Ax = 0.