Question: Let V = R. For u, v E V and a E R define vector addition by ull v := u + v - 1

Let V = R. For u, v E V and a E R define vector addition by ull v := u + v - 1 and scalar multiplication by a Ju := au - a + 1. It can be shown that (V, , D) is a vector space over the scalar field R. Find the following: the sum: 78 -5 the scalar multiple: 407 the zero vector: Ov the additive inverse of a:Let V = R2. For (u1, u2), (v1, v2) E V and a E R define vector addition by (u1, u2) (v1, v2) := (uj + v1 + 3, u2 + 12 + 1) and scalar multiplication by a (u1, u2) := (au + 3a - 3, au2 + a - 1). It can be shown that (V, [, [) is a vector space over the scalar field RR. Find the following: the sum: (0, -5) (-9, -8) the scalar multiple: -1 0(0, -5) = OO the zero vector: Ov the additive inverse of (x, y): (a, y)

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