1.ya.ya Linear spaces
condition: Prove that the set \( M \) of functions \( x(t) \) defined on the domain \( D \) forms a linear space. Find its basis and dimension. \[ \begin{array}{l} M=\left\{a e^{-3 t}+\beta \operatorname{sh} 3 t+\gamma e^{3 t}+\delta\right\} \\ t \in(-\infty,+\infty) \end{array} \]
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.