Q: What is human life expectancy in the United States?
A: Human life expectancy in the United States is 78 years.
Q: Who was president of the United States in 1955?
A: Dwight D. Eisenhower was president of the United States in 1955.
Q: What party did he belong to?
A: He belonged to the Republican Party.
Q: Who was president of the United States before George W. Bush?
A: Bill Clinton was president of the United States before George W. Bush.
Q: Who won the World Series in 1995?
A: The Atlanta Braves won the World Series in 1995.
Q:
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 an eigenvector of a linear transformation f?
A: An eigenvector of a linear transformation f is a vector in the
domain of f that is mapped to itself by f.
Q: What is the definition of a linear transformation?
A: A linear transformation is a mapping from a vector space to itself
that preserves the operations of vector addition and scalar
multiplication.
Q: Is the vector space of univariate polynomials over a finite field a
finite-dimensional vector space?
A: No, the vector space of univariate polynomials over a finite field
is not a finite-dimensional vector space.
Q: What is the maximum number of eigenvalues of an operator on a
5-dimensional vector space?
A: The maximum number of eigenvalues of an operator on a 5-dimensional
vector space is 5.
Q: Can the length of a spanning list for a vector space be longer than
any linearly independent list of vectors in that space?
A: Yes, the length of a spanning list for a vector space can be longer
than any linearly independent list of vectors in that space.
Grading Prompt
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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.
Grade: 3/3
Q: What is a basis of a vector space?
A: A basis of a vector space is a list of vectors that spans the vector space.
Grade: 2/3
Q: What is a basis of a vector space?
A: A basis of a vector space is a linearly independent list of vectors
in the vector space.
Grade: 2/3
Q: What is a basis of a vector space?
A: A basis of a vector space is vectors that fill up the space.
Grade: 0/3
Q: What is a basis of a vector space?
A: A basis of a vector space is a list of vectors that don't depend on
each other.
Grade: 0/3
Q: What is a basis of a vector space?
A: A list of vectors that span the vector space, and none are a linear
combination of the others.
Grade: