(Solution Library) Let A and B be two m * n matrices. Under each of the assumptions below, determine whether A=B must always hold, or whether A=B holds only sometimes.
Question: Let \(A\) and \(B\) be two \(m \times n\) matrices. Under each of the assumptions below, determine whether \(A=B\) must always hold, or whether \(A=B\) holds only sometimes.
- Suppose \(A x=B x\) holds for all \(n\) -vectors \(x\).
- Suppose \(A x=B x\) for some nonzero \(n\) -vector \(x\).
Deliverable: Word Document 
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