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phyxius117
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Homework Statement
Homework Equations
The Attempt at a Solution
I don't know how to do this problem.. Help please!
A basis in linear algebra is a set of linearly independent vectors that span a vector space. This means that any vector in the vector space can be written as a linear combination of the basis vectors. The number of basis vectors is known as the dimension of the vector space.
To determine if a set of vectors form a basis, we need to check two criteria: linear independence and spanning the vector space. Linear independence means that none of the vectors can be written as a linear combination of the others. Spanning the vector space means that every vector in the space can be written as a linear combination of the given vectors. If both criteria are met, then the set of vectors form a basis.
A basis is a set of linearly independent vectors that span a vector space. A spanning set is a set of vectors that span a vector space, but they may not be linearly independent. A basis is a minimal spanning set, meaning that it has the smallest number of vectors needed to span the vector space.
Yes, a vector space can have more than one basis. This is because the dimension of a vector space is not unique to a specific basis. There can be multiple sets of linearly independent vectors that span the same vector space, and each set can be considered a basis.
Bases are used in linear algebra to represent vectors in a vector space. By writing a vector as a linear combination of the basis vectors, we can perform operations such as addition, subtraction, and scalar multiplication. Bases are also used to find the coordinates of a vector and to solve systems of linear equations.