Which of the following would be a linear combination of {(a,b),(c,d)}? (a,b,c,d ≠0)
a) (a,b+d)
b) (a+c,b+d)
c) (a+c,b)
d) (a,d)
Please Help
The answer is b), because
(a,b)+(c,d)=(a+c,b+d). This works for every value of a, b, c and d. The other options CAN be combinations of {(a,b),(c,d)}, but not for every value of a, b, c and d (only for specific ones)