Question: In Exercises, determine if the set of vectors S forms a subspace of the given vector space. Give reasons why S either is or is not a subspace.
Exercise: 1. S is the set of vectors of the form (x1, x2,..., x6) in R6, with the xi real numbers and x1 - x2 + x3 ···+ x6 = 0.
2. S is the set of vectors of the form (x1, x2,..., x5) in R5, with the xi real numbers and x2 3.