(Note: the bold letters are vectors.)
"Suppose that v and w are vectors which are not parallel (so are linearly independent) and the following vector equation holds for some scalars α and β.
v + α(w - v) = β(v + 1/2w).
Find α and β."
With my working out:
-> (1 − α − β) v + (α − β/2)w = 0
-> 1 − α − β = 0 = α − β/2 (by linear independence)
...and from this, I attempted to solve the equations simultaneously but did not get the right answer. (Which was, α = 1/3, β = 2/3)
I really don't understand how you could get that answer either. So, my only problem here is just solving the equations to get the final answer.