Exercise 1.1.7

Question

In the $x y$ plane mark all nine of these linear combinations:
$$
c\left[\begin{array}{l}
2 \
1
\end{array}ight]+d\left[\begin{array}{l}
0 \
1
\end{array}ight] \quad 	ext { with } \quad c=0,1,2 \quad 	ext { and } \quad d=0,1,2
$$

Prakash Anand · Accepted Answer

The nine combinations $c(2,1)+d(0,1)$ with $c=0,1,2$ and $d=(0,1,2)$ will lie on a lattice. If we took all whole numbers $c$ and $d$, the lattice would lie over the whole plane.

Exercise 1.1.7

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Exercise 1.1.7

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