: Checking a system of vectors for linear dependence.

Searching for specific solutions from "Collection of Tasks in Higher Mathematics" (Linear Algebra, Section X) often leads to paid platforms or archives of student-submitted work.

: Determining if a given set forms a linear space.

: Constructing a matrix for a linear transformation in a specific basis.

Because these solutions are extensive mathematical proofs and calculations, they are best viewed on specialized academic resource sites:

: When using these texts, ensure you match the problem statement to your specific textbook edition (1983–2005 or newer), as minor numerical changes sometimes occur between reprints. g., finding the basis in Task 3) for this variant?