Determine whether the subset of C(-∞, ∞) is a subspace of C(-∞, ∞) with the standard operations. Justify your answer.

1. The set of all positive functions: f(x) > 0
2. The set of all constant functions: f(x) = c

Determine whether the subset of Mₙ,ₙ is a subspace of Mₙ,ₙ with the standard operations. Justify your answer.

1. The set of all n × n upper triangular matrices
2. The set of all n × n singular matrices