Prove the statement:
If u, v, and w are linearly independent, then u+v, v, and w are also linearly independent.
Given: $\displaystyle \alpha \vec{u} + \beta \vec{v} + \gamma \vec{w} = \vec{0}$ only when $\displaystyle \alpha = \beta = \gamma = 0$ are equal to zero.
Now re-write $\displaystyle \alpha \vec{u} + \beta \vec{v} + \gamma \vec{w}$ as $\displaystyle \alpha (\vec{u} + \vec{v})+ \delta \vec{v} + \gamma \vec{w} = \vec{0}$ ....