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**Subspaces, Basis, Dimension, Rank**

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Subspace

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Theorem

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Example Let V be the set of all vectors in with length at most 1. Is V a subspace?

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Example Is V a subspace?

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Basis

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Dimension

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Null Space

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Nullity

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Rank Theorem

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Example

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Example

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**Definition of Row and Column Space**

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Theorem

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Theorem

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Example Find the linear relations between the columns.

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Row and Column Rank

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Theorem

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Theorem

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Example Find the rank and the linear relations between the rows.

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**Fundamental Theorem of Invertible Matrices**

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Examples

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