Let $\displaystyle u_{1}, u_{2}$ be nonzero vectors in $\displaystyle R^{n}$ such that $\displaystyle u_{1}u^{T}_{2}=0$.

Show that $\displaystyle u_{1}, u_{2}$ are linearly independent.

I let $\displaystyle u_{1}=(a_{1} a_{2} ... a_{n})$ and $\displaystyle u_{2}=(b_{1} b_{2} ... b_{n})$.

Then $\displaystyle u_{1}u^{T}_{2}=a_{1}b_{1}+a_{2}b_{2}+...+a_{n}b_{n }=0$.

How to continue from here?