Chapter 2 Linear Spaces
We have been focusing on \(\mathbb{R}^3\text{,}\) but what about \(\mathbb{R}^2\text{,}\) can the same things be done there? or \(\mathbb{R}^5\text{?}\) What about any collection that behaves like \(\mathbb{R}^3\) in that elements can be added together and multiplied by real numbers? Examples of such are \(2\times2\) matrices and polynomials. It is a powerful tool to have a small set of elements that, by making linear combinations, can be used to represent the entire collection. This chapter generalizes the important ideas from Chapter 1 on Euclidean Spaces.