I'm reading through the book "Linear Algebra", by Jim Hefferon (which you can download for free!). In section I.3, he describes that the pattern of solutions for a system of linear equations: "They have a vector that is a particular solution of the system added to an unrestrictred combination of some other vectors." Then he goes on to say: "A zero-element solution set fits the pattern since there is no particular solution, and so the set of sums of that form is empty." Isn't he contradicting himself here? First, he says the pattern has a vector of a particular solution, and then he says a zero-element solution fits the pattern because it has no particular solution! Can someone clarify this?