Practical Linear Algebra, 3rd Edition

Chapter 5

2 × 2 Linear Systems

Just about anybody can solve two equations in two unknowns by somehow manipulating the equations. In this chapter, we will develop a systematic way for finding the solution, simply by checking the underlying geometry. This approach will later enable us to solve much larger systems of equations in Chapters 12 and 13. Figure 5.1 illustrates many instances of intersecting two lines: a problem that can be formulated as a 2 × 2 linear system.

Figure 5.1

Intersection of lines: two families of lines are shown; the intersections of corresponding line pairs are marked by black boxes. For each intersection, a 2 × 2 linear ...