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Text Generator > Use Cases >Question Answering - Text Generator API

### Question Answering - Text Generator API

#### Example input

• Q: What is the definition of a linearly independent list? A: A linearly independent list is a list of vectors that cannot be expressed as a linear combination of other vectors in the list. Q: What is a basis of a vector space? A: A basis of a vector space is a linearly independent list of vectors that spans the vector space. Q: What is a spanning list of vectors in a vector space? A: A spanning list of vectors in a vector space is list of vectors in the vector space such that every vector in the vector space can be written as a linear combination of the vectors in the spanning list. Q: What is the definition of a linear transformation? A:

#### Example real generated results

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A linear transformation T: V --> W consists of two parts: an n by m matrix M and an m-vector t. M is called the map or matrix, and t is known as the translation or coefficient vector. Answer not in context A linearly dependent list is a list of vectors that cannot be expressed as a linear combination of other vectors in the list. -- wikipedia definition of a linearly independent list? a list of vectors that cannot be expressed as a linear combination of other vectors in the list

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A linear transformation T from V to W is an application with the property that for all u and v, u = T(v) if and only if uv = 0 Note: This is not homework - this is ACTUAL TEST QUESTIONS! definition of a linear transformation? A: A linear transformation T from V to W is an application with the property that for all u and v, u = T(v) if and only if uv = 0 Yes - No 1. no 2.

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A linear transformation is an operator that maps one set of vectors to another. it preserves the rank and the dimension. so if two sets of vectors are related by a linear transformation, they will have equivalent representations as lists of numbers. It also preserves the inner product between the corresponding pairs of vectors.

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A linear transformation is an invertible mapping from one vector space to another." - definition is -, meaning that it maps each member of a set into exactly one member of some other set definition of a linear map - if and only if for any given vector x, there exists y such that.x = y + b where.y is said to be defined by the equation y = ax + c for some integer a,b,c and known constants. - note - not all definitions