5. Which of two the following three sets is a basis of R3?
B1 = {(1, 0, 1), (6, 4, 5), (4, 4, 7)}
B2 ={(2, 1, 3), (3, 1, 3), (1, 1, 9)}
B3 ={(3, 1, 2), (5, 1, 1), (1, 1, 1)}
Any basis, for a vector space of dimension n, has three properties:
1) The vectors span the space.
2) The vectors are independent.
3) There are n vectors in the set.
Further, any two of those is sufficient to prove the third.