Question

Let V=(-9, [infinity]). For u, v ∈ V and a ∈ R define vector addition by u ± t v:=u v+9(u+v)+72 and scalar multiplication by a □ u:=(u+9)ᵃ-9. It can be shown that (V, BH, [) is a vector space over the scalar field R. Find the following the sum: −2Ri−8=___

Answer 1

The question appears to involve vector spaces with undefined operations ± and □, which aren't standard in vector algebra. In standard algebra, vector addition and subtraction involve adding or subtracting corresponding components, and scalar multiplication involves multiplying each vector component by a scalar.

Step-by-step explanation:

The question you're asking seems to be about vector spaces and operations defined on them, but the question is unclear about the operation ± and the box symbol □ they're not standard vector operations. However, based on the typical operations in vector algebra, we can discuss the sum and difference of two vectors A and B, as well as scalar multiplication. To find the sum ℝ = ᵁ + B, you add the corresponding components of the vectors: ℝx= Ax + Bx, ℝy = Ay + By, etc.. For the difference, we define Đ = A - B, which is equivalent to Đ = A + (-B), performed by subtracting the corresponding components. Scalar multiplication a ℝ involves multiplying each component of the vector ℝ by the scalar a.