1.ya.12 Linear spaces
Condition: Does a linear space form a given set in which the sum of any two elements \( x \) and \( y \) and the product of any element \( x \) by any real number \( \alpha \) are defined? The set of all vectors of space \( \mathbb{V}_{3} \) lying on the same axis; sum: \( x+y \), product \( \alpha|x| \).
Linear spaces, subspaces. Investigation of given sets with operations defined on them to compose a linear space. Axioms of linear spaces. Linear spaces of polynomials, matrices, vectors, functions and numbers.