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Chapter1Systems of Linear Equations: Algebra

Primary Goal

Solve a system of linear equations algebraically in parametric form.

In this chapter we study systems of linear equations and their solutions algebraically. We will learn a systematic way to solve systems of equations of the form

ADCDB 3 x 1 + 4 x 2 + 10 x 3 + 19 x 4 − 2 x 5 − 3 x 6 = 1417 x 1 + 2 x 2 − 13 x 3 − 7 x 4 + 21 x 5 + 8 x 6 = 2567 − x 1 + 9 x 2 + 3 2 x 3 + x 4 + 14 x 5 + 27 x 6 = 26 1 2 x 1 + 4 x 2 + 10 x 3 + 11 x 4 + 2 x 5 + x 6 = − 15.

In Section 1.1, we introduce systems of linear equations, the heart of linear algebra. In Section 1.2, we present a procedure, called row reduction, for finding all solutions of a system of linear equations. In Section 1.3, we show how to express all solutions of a system of linear equations using the parametric form of the general solution.