Consider the following sets of vectors in R3:
S1 = { (3, -2, -3), (0, 4, 2), (0, 1, 3) }
S2 = { (-2, 3, 4), (2, 4, -3), (4, 3, -3), (4, 3, -2) }
S3 = { (0, -3, -4), (0, -12, 0), (0, 6, -12) }
S4 = { (-2, 2, 3), (4, -2, 3) }
You are asked to determine which of these sets are bases for R3. For each of the following statements, select True or False to indicate your answer.
1. The set S1 is a basis for R3.
2. The set S2 is a basis for R3.
3. The set S3 is a basis for R3.
4. The set S4 is a basis for R3.
