Is {(1, 1, 1, (0, 1, 1), (0, 0, 1)} a basis for R3? Is {(1, 0,

Question:

Is {(1, 1, 1, (0, 1, 1), (0, 0, 1)} a basis for R3? Is {(1, 0, 0), (0, 1, 0), (0, 0, 1)}?
A linear space which has a basis with a finite number of elements is said to be finite dimensional. Otherwise, the linear space is called infinite dimensional. In a finite-dimensional space X, every basis has the same number of elements, which is called the dimension of X and denoted dim X.