For more Linear Algebra content, there are complete textmaps for "Linear Algebra" by Schilling, Nachtergaele and Lankham and "Linear Algebra" by Waldron, Cherney, & Denton.
- An m by n matrix is an array of numbers with m rows and n columns.
- 3: Linear Systems
- We know that for two by two linear systems of equation, the geometry is that of two lines that either intersect, are parallel, or are the same line. If they intersect then there is exactly one solution, if they are parallel then there are no solutions, and if they are the same line, then there are infinitely many solutions. For three by three systems, the situation is different. The solution set is either the empty set, a point, a line, or a whole plane.