Linear Independence
The only solution to
Geometric Interpretation
If two vectors are linearly independent, the are not colinear If 3, then not coplanal If 4, not cospacial
Linear Dependence
- Any of the vectors in the set are a linear combination of the others
- If there is a free variable, so there are infinite solutions to the homogenous equation
- If the columns of A are in
, and there are basis vectors in (which is always true), then if the amount of columns in A exceeds the amount of basis vectors that exist in that dimension, it means that there are free variables, which indicates linear dependence - If one or more of the columns of A is
- Iff