1.ya.17 Linear spaces
condition: Find the orthogonal basis \( L \), if \( L=\wedge\left(a_{1}, a_{2}, a_{3}\right), \quad a_{1}=(0,2,1,-1) \), \( a_{2}=(1,0,2,3), \quad a_{2}=(1,4,4,1) \quad \) (linear span of vectors).
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.