Vector Spaces

Practice: Verifying Vector Space Axioms

Let V={(x,y)    x,yR}V=\{(x,y)\;|\;x,y\in\mathbb{R}\} and define the following operations:
  • (u1,u2)+(v1,v2)=(u1+v1+1, u2+v2+1)(u_1,u_2)+(v_1,v_2)=(u_1+v_1+1,\ u_2+v_2+1)
  • k(v1,v2)=(kv1,kv2)k\cdot(v_1,v_2)=(kv_1,kv_2)
Determine which of the following vector space axioms, if any, are satisfied. [Select all that apply]
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