Linear Algebra: Theory and Applications, 2nd Edition

CHAPTER ONE Systems of Linear Equations

1.1 SOLVING SYSTEMS OF LINEAR EQUATIONS

Do not worry about your difficulties in mathematics. I can assure you that mine are still greater.

—ALBERT EINSTEIN (1879–1955)

Begin at the beginning and go until you come to the end: then stop.

—LEWIS CARROLL (1832–1889), ALICE’S ADVENTURES IN WONDERLAND

The term linear algebra applies to a branch of mathematics that studies vectors, matrices, vector spaces, and systems of linear equations. It is hoped that the reader has acquaintance with some of these terms. For example, a vector with three components looks like (2.5, 3.7, −5.1), while a 2 × 3 matrix looks like this:

These two building blocks, vectors and matrices, can produce systems of linear equations, and these ...