The computational aspect of this course has been based on one crucial observation: Row operations do not change the solutions to a system of linear equations. This would be a silly place to lose points on an exam. So the next time you"re eating alone, get a sheet of paper and perform some row reductions. Check if they are correct by using wolfram alpha: describe a solution set for a system of linear equations the solutions to a system of linear equations of the form = 0 in n-variables forms a subspace of rn. Be able to nd a basis for such a subspace: eliminating redundancies if you are presented with a subspace of rn described as the span of some vectors, be able to nd a basis for that subspace. [recall that we showed these facts in low dimensions by using row reduction] It"s good to know how to do the technical stu .