ABSTRACT
Linear algebra arises throughout mathematics and the sciences. The most basic problem in linear algebra is to solve a system of linear equations. The unknown can be a vector in a finite-dimensional space, or an unknown function, regarded as a vector in an infinite-dimensional space. This chapter begins by reviewing methods for solving both matrix equations and linear differential equations. When there are finitely many equations in finitely many unknowns, the chapter solves using row operations, or Gaussian elimination. The chapter illustrates by discussing a simple Kakuro puzzle. Kakuro is a puzzle where one is given a grid, blank squares, the row sums, the column sums, and blacked-out squares. It provides an informal discussion of linear equations in general circumstances. Equality of numbers provides the simplest example of an equivalence relation, but it is too simple to indicate why the concept is useful.
