Please answer the question below and clearly shows the steps. No need to rush. Just try your best.

1. Consider the set F", with an alternative vector addition defined as V1 W1 v1 + W1 - v1W1 U2 W2 v2 + W2 - V2W2 = Un + Wn - Un Wn and alternative scalar multiplication defined as U1 2 01 U2 C2 V2 CO = Is Fr, equipped with these two operations, a vector space? If so, prove it. If not, describe exactly which vector space axioms are not satisfied, and give counterexamples to each. Also state which vector space axioms are satisfied, and prove those