1.ya.13 Linear spaces
Condition: Let \( V \) be the linear space of all polynomials over \( \mathbb{R} \) of degree \( \leq 5 \), and let \( v \) be the bilinear form on \( V \) given by the formula \( \quad v(p, q)=\sum_{k=1}^{n} p(k) q(k) \). For what values of \( n \) is the form \( v \) a scalar product of \( V \)?
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.