Sufficient Conditions for Basis of Finite Dimensional Vector Space/Examples
Jump to navigation
Jump to search
Examples of Use of Sufficient Conditions for Basis of Finite Dimensional Vector Space
Example: $2$ Dimensions
Let $V$ be a vector space of $2$ dimensions.
Let $\mathbf u, \mathbf v \in V$ be vectors
Let $\mathbf u$ and $\mathbf v$ be such that neither $\mathbf u$ nor $\mathbf v$ is a scalar multiple of the other..
Let $\mathbf w \in V$.
Then there exist scalars such that:
- $\mathbf w = a \mathbf u + b \mathbf v$