Question

Let V = R. For u, v in V and a in R, define vector addition by u ⊕ v = u + v + 2 and scalar multiplication by a * u = au + 2a - 2.

Answer 1

This question is about vector addition and scalar multiplication in the vector space V=R.

Step-by-step explanation:

In this question, the operations of vector addition and scalar multiplication are defined for the vector space V=R.

1. Vector addition is defined as u ⊕ v = u + v + 2, where u and v are vectors in V.
2. Scalar multiplication is defined as a * u = au + 2a - 2, where a is a scalar and u is a vector in V.

These definitions allow us to perform addition and multiplication operations using the given vectors and scalars in the vector space V=R.