1. ## Basis

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

2. Originally Posted by Apprentice123 Find a basis for $\displaystyle R^4$ includes the vectors: $\displaystyle (1,0,1,0)$ and $\displaystyle (0,1,-1,0)$
Does $\displaystyle (1,0,0,0)\;\&\;(0,0,0,1)$ do it?
How would you prove or disprove it?

3. Originally Posted by Plato Does $\displaystyle (1,0,0,0)\;\&\;(0,0,0,1)$ do it?
How would you prove or disprove it?

I did not understand

4. Originally Posted by Apprentice123 I did not understand
What is there to understand?
Do you know what a basis is?
Do you know what properties are required?

5. 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.

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