For the matrix B below, find sets of vectors whose span equals the column space of B (C(B)) and which individually meet the following extra requirements.
1. The set illustrates the definition of the column space.
2. The set is linearly independent and the members of the set are columns of B.
3. The set is linearly independent with a "nice pattern of zeros and ones" at the top of each vector.
4. The set is linearly independent with a "nice pattern of zeros and ones" at the bottom of each vector.

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2 3 1 1 B=1110 1 2 3 4