Question

which is not a vector space​

Answer 1

Answer:

the first quadrant of the plane is not a vector space

Step-by-step explanation:

A vector space, also known as a linear space, is a set whose components, sometimes termed vectors, may be added to and multiplied ("scaled") by figures known as scalars. Real numbers make up scalars most of the time, but they can also be complex numbers or, more broadly, components of any field. Certain conditions, referred to as vector axioms, must be met by the operations of vector addition and scalar multiplication. Real coordinate space or complex coordinate space are two phrases that are frequently used to describe the nature of the scalars.

• Parallel to this, the first quadrant of the plane (although containing the coordinate axes and the origin) is not a vector space since a vector space has to enable any scalar multiplication, including negative scalings.
• The positive real numbers are not considered to be a field in this construction since they lack an additive identity or inverses.
• Fields are formed of "numbers," but vector spaces are made of "collections of numbers," to put it broadly (vectors). Any two numbers may be multiplied together, and you can multiply a group of integers using a single fixed number. A field is created by complex numbers.
• The operations of the field and the vector space are separate from those of the scalar multiplication, which involves both field and space in addition to having its own operations.

hence  the first quadrant of the plane is not a vector space