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Proof Paradise

Theorem 2

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Theorem If $T:\mathbf{R}^n\rightarrow\mathbf{R}^m$ is a linear function, then $T(\vec{0})=\vec{0}$.

Theorem 1

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Theorem If $x,y\in \mathbf{R}^2$ and one is not a multiple of the other, then every vector in $\mathbf{R}^2$ is a linear combination of $x$ and $y$.

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