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SMG75
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Homework Statement
Suppose x, y [itex]\in\Re^{n}[/itex] are nonparallel vectors.
a) Prove that if sx+ty=0, then s=t=0
b) Prove that if ax+by=cx+dy, then a=c and b=d
Homework Equations
The Attempt at a Solution
I'm very new to proof-based math, so I'm just trying to get my feet wet here. I realize this is a very simple problem, but I was hoping someone could walk me through it.
Assuming s[itex]\neq[/itex]0, then sx=-ty. Thus, x=(-t/s)y, which goes against the definition of nonparallel vectors. (Two vectors are parallel if they can be written with scalar constant. i.e. x=cy or y=cx). So, as a result, we know s[itex]\neq[/itex]0 must not be possible. Using similar logic, t=0 cannot be possible, either. Therefore, s=t=0.
I realize this is incredibly rough; I'm just looking to see if my thinking is on the right track.
Thanks!