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Class 10 > Learn UNIT II: Algebra > What is a basis in linear algebra?
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What is a basis in linear algebra?

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a set B of vectors in a vector space V is called a basis ( pl. : bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B.
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Mathematics (from 9th to 12th) and Science(9th and 10th) Home Tutor , I have experience of 5 years

Basis is a collection of Linearly independent vector that can span the whole vector space. Also it is largest Linearly independent set and smallest spanning set
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In mathematics, a set B of vectors in a vector space V is called a basis ( pl. : bases)
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In linear algebra, a basis of a vector space is a set of linearly independent vectors that span the vector space. This means that every vector in the vector space can be written as a unique linear combination of the vectors in the basis. The number of vectors in a basis is called the dimension of the...
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In linear algebra, a basis of a vector space is a set of linearly independent vectors that span the vector space. This means that every vector in the vector space can be written as a unique linear combination of the vectors in the basis. The number of vectors in a basis is called the dimension of the vector space.

There are many different bases for a vector space, but all bases for the same vector space have the same number of vectors. This number is called the dimension of the vector space. 

 

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In mathematics, a set B of vectors in a vector space V is called a basis ( pl. : bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect...
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In mathematics, a set B of vectors in a vector space V is called a basis ( pl. : bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. 

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a basis is a set of vectors that can be used to represent any vector in a vector space
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"Transforming Numbers into Knowledge: 5 Years of Inspiring Mathematical Excellence"

In linear algebra, a basis is linearly independent spanning set that spans the whole space.
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