Prove the statement:

Ifu,v, andware linearly independent, thenu+v,v, andware also linearly independent.

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- Dec 21st 2008, 05:34 PMssl000Prove linearly independent
Prove the statement:

If**u**,**v**, and**w**are linearly independent, then**u+v**,**v**, and**w**are also linearly independent. - Dec 21st 2008, 05:54 PMmr fantastic
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 $\displaystyle \alpha (\vec{u} + \vec{v})+ \delta \vec{v} + \gamma \vec{w} = \vec{0}$ .... - Dec 21st 2008, 06:44 PMssl000
- Dec 21st 2008, 10:02 PMmr fantastic