1. Linear Spaces
Condition: to prove that many \ (m \) functions \ (x (t) \) specified in the area \ (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 \ \} \\ 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.