homework - Basis for $\mathbb{Z}^2$ - Mathematics - Stack Exchange
(Yes, you're right)
Find conditions on a, b, c, d for {(a, b), (c, d)} to be a basis for . [Hint: Solve x(a, b) + y(c, d) = (e, f) in , and see when the x and y lie in .]
My solution:
x(a, b) + y(c, d) = (e, f)
ax + cy = e
bx + dy = f
x = (ed - fc)/(ad - bc)
y = (af - be)/(ad - bc)
Since x and y , is the required condition.
Am I right?
homework - Basis for $\mathbb{Z}^2$ - Mathematics - Stack Exchange
(Yes, you're right)