- #1
SithsNGiggles
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Homework Statement
I hope this is the right place to post this.
For my linear algebra homework, I have to prove that
"If [itex]\vec{u} \neq \vec{0}[/itex] and [itex]a\vec{u} = b\vec{u}[/itex], then [itex]a = b[/itex]."
Homework Equations
The Attempt at a Solution
I'm trying to prove the contrapositive, but I'm not sure how to alter the statement.
I think it's something like
"If [itex]a \neq b[/itex], then [itex]\vec{u}=\vec{0}[/itex] or [itex]a\vec{u} \neq b\vec{u}[/itex]."
But then I don't know where to begin, so I'm guessing a proof by contrapositive isn't the right method to use here. It seems to me that a direct proof might me simpler, but I guess I wanted to challenge myself. Any ideas? Thanks.