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.
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?