Sufficient Conditions for Basis of Finite Dimensional Vector Space/Examples/2 Dimensions
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Examples of Use of Sufficient Conditions for Basis of Finite Dimensional Vector Space
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:
- $\mathbf w = a \mathbf u + b \mathbf v$
Proof
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Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): $\text{A}.2$: Linear algebra and determinants: Corollary $\text{A}.8$