Solution Preserving Operations

Earlier, while defining linear systems, we discussed the different possibilities of the solution of a linear system. In this chapter, we’ll describe how we can achieve those possibilities. Let’s start by learning the foundations before moving on to a systematic approach.

Augmented matrix

We’ve already learned two different representations of a system of linear equations. We started with a set of linear equations, that is,

$$a_{11}x_1 + a_{12}x_2+...+ a_{1n}x_n = y_1$$

$$a_{21}x_1 + a_{22}x_2+...+ a_{2n}x_n = y_2$$

$$\vdots$$

$$a_{m1}x_1 + a_{m2}x_2+...+ a_{mn}x_n = y_m$$ ...