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Let V = (-4, infinity). For u, v belongs to V and a belongs to R define vector a

ID: 3120465 • Letter: L

Question

Let V = (-4, infinity). For u, v belongs to V and a belongs to R define vector addition by u Squared Plus v: = uv + 4(u + v) + 12 and scalar multiplication by a squared dot operator u: = (u + 4)^a - 4. It can be shown that (V, squared plus, Squared Dot Operator) is a vector space over the scalar field, R. Find the following: the sum 2 Squared Plus -1 = ________________ the scalar multiple: -5 Squared Dot Operator 2 = _______________ the additive inverse of 2: Squared Minus 2 = ________________ the zero vector: 0_v = _______________ the additive inverse of x: Squared Minus x = ___________________

Explanation / Answer

A.2+(-1)=2(-1)+4(2-1)+12=14.

B.-5*2=(2+4)^-5 -4=(6)^-5-4=(1/6^5)-4.

C.let v be additive inverse of 2,then 2+v=0=>2v+4(2+v)+12=0=>6v+20=0=>v=-20/6.

D.zero vector =0.

E.Additive inverse of x be y,then x+y=0=>xy+4(x+y)+12=0=>y(x+4)=-(4x+12)=>y=-(4x+12)/(x+4).