Question Answering - Text Generator API

Question Answering API - answer quewstions with the 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 from one vector space to another is a map that preserves the operations of addition and scalar multiplication. Q: How do you determine if two matrices are similar? A: Two matrices are similar if they represent the same linear transformation with respect to different bases, i.e., there exists an invertible matrix P so that A = PBP^(-1). */ public class VectorSpaceOperations { /** * Constructs a new instance

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  A linear transformation from one finite dimensional vector space to another is a function f : V → W between two vector spaces, where for all u and v in V and c in R, we have f(u + cv) = cf(u). The following are equivalent definitions: 1.) For any u and v in V, (u + v) ∈ Img(f), so Img(f) ⊆ V'

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  A linear transformation from one vector space to another is an invertible function between them, which preserves addition and scalar multiplication. Q: How do you prove two sets are equal? A: To show that two sets are equal, we must demonstrate they contain exactly the same elements; therefore, for any element x, if it belongs to set A, then it also belongs to set B, and vice versa. What are some key differences between these topics?

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  A linear transformation is a function between two finite-dimensional vector spaces that preserves addition and scalar multiplication. Q: How does one define an inner product on a vector space? A: An inner product on a vector space is a way to assign a real number to each pair of vectors, satisfying certain properties (closure, linearity, positive definiteness). The most common example is the dot product for Euclidean n-space.

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