About: Linear independence   Sponge Permalink

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A set of vectors is linearly independent if no vector in the set can be expressed as a linear combination of the other vectors. For example, the vectors are linearly independent. If vectors are linearly independent, they form the basis for a vector space. If the zero vector is in a set of vectors, they cannot be linearly independent, since zero times any vector is the zero vector.

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  • Linear independence
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  • A set of vectors is linearly independent if no vector in the set can be expressed as a linear combination of the other vectors. For example, the vectors are linearly independent. If vectors are linearly independent, they form the basis for a vector space. If the zero vector is in a set of vectors, they cannot be linearly independent, since zero times any vector is the zero vector.
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  • A set of vectors is linearly independent if no vector in the set can be expressed as a linear combination of the other vectors. For example, the vectors are linearly independent. If vectors are linearly independent, they form the basis for a vector space. If the zero vector is in a set of vectors, they cannot be linearly independent, since zero times any vector is the zero vector.
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