2: Vectors, matrices, and linear combinations
We began our study of linear systems in Chapter 1 where we described linear systems in terms of augmented matrices, such as
\[
\left[\begin{array}{rrr|r}
1 & 2 & -1 & 3 \\
-3 & 3 & -1 & 2 \\
2 & 3 & 2 & -1
\end{array}\right]
\]
In this chapter, we will uncover geometric information in a matrix like this, which will lead to an intuitive understanding of the insights we previously gained into the solutions of linear systems.