- #1
Destroxia
- 204
- 7
Homework Statement
In the xy-plane mark all nine of these linear combinations:
## α \lbrack 2, 1 \rbrack + β \lbrack 0, 1 \rbrack## with c = 0, 1, 2 and d = 0, 1, 2
Homework Equations
ANSWER:
The nine combinations will lie on a lattice. If we took all whole numbers c and d, the lattice would
lie over the whole plane.
The Attempt at a Solution
I think my biggest problem in this, is not actually knowing what the question is asking.
I've tried plotting the linear combinations of me filling in α and β with the numbers listed for c & d.
1. ## 0 \lbrack 2, 1 \rbrack + 0\lbrack 0, 1 \rbrack ## yields, ## \lbrack 0, 0 \rbrack ##
2. ## 1 \lbrack 2, 1 \rbrack + 1\lbrack 0, 1 \rbrack ## yields, ## \lbrack 2, 2 \rbrack ##
3. ## 2 \lbrack 2, 1 \rbrack + 2\lbrack 0, 1 \rbrack ## yields, ## \lbrack 4, 4 \rbrack ##
I'm not sure where they are getting 9 linear combinations, but I'm pretty sure I'm misunderstanding the instructions of the problem.