Subspace

Definition:

• The possible position vector occupied by $n$ vectors by a Linear Combination
• In $R^3$, 2 independent vectors have subspace of $R^2$
• Vector Space is a subspace of its self

Properties:

• Contains the origin
• Closure under addition and scalar multiplication:
  • A nonempty subset, $V$ of a Vector Space $\chi$ if for any scalars, $\alpha ,\beta :x,y\in V⟹\alpha x+\beta y\in V$
  • A nonempty subset, $V$ of a Vector Space $\chi$ if for any scalars, $\alpha ,\beta :x,y\in V⟹\alpha x\ast \beta y\in V$