Find a basis for $\displaystyle R^4$ includes the vectors: $\displaystyle (1,0,1,0)$ and $\displaystyle (0,1,-1,0)$

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- Nov 15th 2008, 08:05 AMApprentice123Basis
Find a basis for $\displaystyle R^4$ includes the vectors: $\displaystyle (1,0,1,0)$ and $\displaystyle (0,1,-1,0)$

- Nov 15th 2008, 09:32 AMPlato
- Nov 15th 2008, 09:46 AMApprentice123
- Nov 15th 2008, 10:21 AMPlato
- Nov 15th 2008, 12:08 PMScopur
Remember a basis is a linear independent spanning set. A Basis of $\displaystyle \mathbb{R}^4$ is going to consist of 4 linear independent vectors. So all you do is take the 2 vectors they gave you and find 2 other linear independent vectors. As Plato suggested just take 2 vectors from the standard basis and see if they are linear independent.