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## Homework Statement

Is the system of vectors a1=(1,-1,0,1), a2=(2,3,-1,0), a3=(4,1,-1,4) linearly independent? Do these vectors form a basis in the vector space

**R^4**? State why.

## Homework Equations

## The Attempt at a Solution

I have done the first part of the exercise. I have found that the system of vectors is linearly independent and the rank is 3. I think that if there are 3 linearly independent vectors, and the rank is 3, then the vectors will form a basis in vector space

**R^3**. What about

**R^4**? How to prove whether it does form the basis?