Question

) In R, consider the addition x ⊕ y = x + y − 1 and a.x = a(x − 1) + 1. Show that R is a real
vector space with respect to these operations with additive identity 1

Answer 1

Answer:

) In R, consider the addition x ⊕ y = x + y − 1 and a.x = a(x − 1) + 1. Show that R is a real

vector space with respect to these operations with additive identity 1

Step-by-step explanation:

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Answer 2

Answer:

To check that V is a vector space, one must check each of the 10 axioms of a vector space to see if they hold. (a, b)+(c, d) = (2(a + b + c + d), −1(a + b + c + d)) ∈ V. Therefore V is closed under addition (A1 holds).

Step-by-step explanation:

A vector space is a set that is closed under addition and scalar multiplication. Definition A vector space (V, +,., R) is a set V with two operations + and · satisfying the following properties for all u, v 2 V and c, d 2 R: (+i) (Additive Closure) u + v 2 V . Adding two vectors gives a vector.

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