Question

Suppose you have R² and the + (addition) operation is as follows: (a, b) + (c, d) = (a+d,b+c). alar multiplication is defined in the usual way. This is a vector space.

A. True
B. False

Answer 1

The addition and scalar multiplication operations in this vector space satisfy the required properties for a vector space.

Step-by-step explanation:

Addition and Scalar Multiplication in Vector Space

In this vector space, the addition operation is defined as follows: (a, b) + (c, d) = (a+d, b+c). This means that when you add two vectors in this vector space, you simply add their corresponding components.

Scalar multiplication in this vector space is defined in the usual way.

Since the addition and scalar multiplication operations have the required properties for a vector space, namely associativity, commutativity, and distributivity, the statement is true. This vector space is indeed a vector space.