If S Spans a Vector Space V, but S Is

question 3

True/False

If S spans a vector space V, but S is not linearly independent in V, then there exists a vector v in S such that the set difference also spans V.

---

Definitions:

Dependent Children

Individuals, typically under the age of 18, who rely on adults for financial support and care.

Excise Tax

Taxes applied to specific goods, services, or activities, either as a flat amount per unit or as a percentage of the price.

Direct and Indirect

Terms used to differentiate between costs, taxes, or subsidies that are explicitly linked to the production or sale of a good (direct) and those that are not directly linked but influence economic outcomes (indirect).

Federal Expenditures

Spending by the federal government of a country, including costs for defense, welfare, infrastructure, and other public services.