There are objects in mathematics which can be added together as well as multiplied by numbers also, like polynomials, matrices, real valued functions etc. In these systems, the operations of addition and multiplication by numbers have properties which are the same as those of ℝ^{n} as given in chapter. The elements of ℝ^{n} are called vectors and the real numbers are called scalars. For this reason, an algebraic structure which has ℝ^{n}, like properties is called a vector space. In this chapter, we define and study vector spaces. A good intuitive model for a vector space is provided by ℝ^{2} and ℝ^{3}.

**Definition 13.1.** *( Vector space): Let V be a non-empty set and F a field. Let a binary operation + be ...*

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