which of the following vectors are spaces {[1 0 0 1], [0 1 0 0], [1 1 1 1],[0 1 1 1]}

The set of vectors you provided is a subset of R^4 (four-dimensional real number space). To determine if this set forms a vector space, we need to check if it satisfies the following properties:

1. Closure under addition: If we add any two vectors in the set, the result should also be in the set.
2. Closure under scalar multiplication: If we multiply any vector in the set by a scalar, the result should also be in the set.
3. The set contains the zero vector.

Let's check these properties:

1. Closure under addition: If we add [1 0 0 1] and [0 1 0 0], we get [1 1 0 1], which is not in the set. So, the set is not closed under addition.

2. Closure under scalar multiplication: If we multiply [1 0 0 1] by 2, we get [2 0 0 2], which is not in the set. So, the set is not closed under scalar multiplication.

3. The set does not contain the zero vector [0 0 0 0].

Therefore, the set of vectors {[1 0 0 1], [0 1 0 0], [1 1 1 1],[0 1 1 1]} does not form a vector space.