3.13. Explorations

This section covers some ideas which I need to pursue further

HK p. 34, Sec. 2.1 Ex. 4

Let \(V\) be the set of all pairs \((x,y)\) of real numbers, and let \(F\) be the field of real numbers. Define

\[ \begin{align}\begin{aligned}(x,y) + (x_1, y_1) = (x + x_1, y + y_1)\\c(x,y) = (cx,y)\end{aligned}\end{align} \]

• Verify that this is a vector space.

• Whats the use of this system in engineering?