Question: Show that V = {(a, b) a, b R} with addition defined by (a1, a2)+(b1, b2) = (a1b1, 0) and scalar multiplication is defined as

  1. Show that V = {(a, b) a, b R} with addition defined by (a1, a2)+(b1, b2) = (a1b1, 0)
  2. and scalar multiplication is defined as c(a1, a2) = (ca1, ca2) is not a vector space. In
  3. addition list all of the axioms that fail.

Show that V = {(a, b) a, b R} with addition defined

(7) Show that V = {(a, b) | a, be R } with addition defined by (a1, a2) + (b1, b2) = (a1b1, 0) and scalar multiplication is defined as c(a1, a2) = (cal, ca2) is not a vector space. In addition list all of the axioms that fail

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