1. Basis

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

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

3. Originally Posted by Plato
Does $(1,0,0,0)\;\&\;(0,0,0,1)$ 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 $\mathbb{R}^4$ 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.