How to convert from Object space into World space (exercise from 3D Math Primer book)
For others who might have this question, here a perhaps more straight forward numeric answer (I'm now working myself on this book as well). Consider that:


We are given object space coordinates that need to be transformed into upright and subsequently world space coordinates.
We know that a vector $\vec{v}$ can be represented as a linear transformation of its axises in relation to the set of basis vectors $\vec{p}$, $\vec{q}$, $\vec{r}$, when these are orthonormal (perpendicular to each other and with length $l = 1$)
The equation to represent this is thus: $\vec{v} = v_{x}p + v_{y}q + v_{z}r$ 
Given the basis vectors we can computed this for each object reference using the above equation. So, the first example would be:


$\vec{u} = -1 \begin{bmatrix}0.866\\ 0\\ -0.500 \end{bmatrix} + 2 \begin{bmatrix}0\\ 1\\ 0\end{bmatrix} + 0 \begin{bmatrix}0.500\\ 0\\ 0.866\end{bmatrix} = \begin{bmatrix}-0.866\\ 2\\ 0.500\end{bmatrix}$

Then, to compute this in world space, you simply need to add your world space reference to the upright vector. Meaning:

$\vec{w} = o + u$

For the first example in the book that would be:

$\vec{w} = \begin{bmatrix}1\\ 10\\ 3\end{bmatrix} + \begin{bmatrix}-0.866\\ 2\\ 0.500\end{bmatrix} = \begin{bmatrix}0.134\\ 12\\ 3.500\end{bmatrix}$