# Basis

• Nov 15th 2008, 08:05 AM
Apprentice123
Basis
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 AM
Plato
Quote:

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?
• Nov 15th 2008, 09:46 AM
Apprentice123
Quote:

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
• Nov 15th 2008, 10:21 AM
Plato
Quote:

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?
• Nov 15th 2008, 12:08 PM
Scopur
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.