Objectives
- Equivalent linear system.
- Three row operations.
- Matrix equation.
Chapter 1 System of linear equations
Motivation: Find the all values of \(x,y,z\) which satisfy the equations below.
\begin{align*}
3y+4z\amp=11\\
3x-7y+4z\amp=4\\
3x-9y+6z\amp= 6
\end{align*}
From this example, we will learn the idea how to solve this example, that is, to obtain an equivalent system through three elementary row operations. Moreover, we introduce a notion \(A\mathbf{x}=\mathbf{b}\text{,}\) which begins the era of matrix theory.
