Let denote the set of ordered triples and define addition in as in . For each of the following definitions of scalar multiplication, select all properties of scalar multiplication for vector spaces that hold and decide whether is a vector space.
(a)
Select all properties of scalar multiplication that hold true.

Is a vector space?

(b)

Select all properties of scalar multiplication that hold true.

Is a vector space?

(c)

Select all properties of scalar multiplication that hold true.

Is a vector space?

(d)

Select all properties of scalar multiplication that hold true.

Is a vector space?

Source

[Nicholson] W. Keith Nicholson, Linear Algebra with Applications, Lyryx 2021, Open Edition, Exercises 6.1.1.

2024-09-06 02:08:44