Question:
Subspaces of the Vector Space of 2-by-2 Matrices
Please use formal proofs and language where applicable, and be sure to explain your reasoning thoroughly.
Please post response as a Word or PDF file.
1. Let A be a particular vector in ℜ2x2. Determine whether the following are subspaces of ℜ2x2:
A. S1 = { B∈ℜ2x2|BA = 0}
B. S2 = { B∈ℜ2x2|AB ≠BA}
C. S3 = { B∈ℜ2x2|AB + B = 0}