math.la.e.linsys.3x3.soln.row_reduce.z
A 3x3 matrix equation Ax=b is solved for two different values of b. In one case there is no solution, and in another there are infinitely many solutions. These examples illustrate a theorem about linear combinations of the columns of the matrix A.
The reduced row echelon form is used to determine when a 3x3 system is inconsistent. A picture of planes in 3-dimensional space is used to provide geometric intuition.