10 Questions
Which set denotes the vector space of all linear transformations from V to W?
L(V, W)
What is the formula for (f + g)(v)?
(f + g)(v) = f(v) + g(v)
What is the formula for (k · f)(v)?
(k · f)(v) = k · f(v)
What is the dimension of the vector space L(V, W) if dim V = n and dim W = m?
mn
What is the zero vector in L(V, W)?
The zero transformation
Which one of these is the most correct?
The set of all linear transformations from V to W is denoted by L(V, W)
Which one of these is the most correct?
(f + g)(v) = f(v) + g(v)
Which one of these is the most correct?
(k · f)(v) = k · f(v)
Which one of these is the most correct?
The zero vector in L(V, W) is the zero transformation
Which one of these is the most correct?
The dimension of the vector space L(V, W) is mn if dim V = n and dim W = m
Test your knowledge on dual spaces, eigenvectors, and eigenvalues in this quiz. Learn about the vector space of linear transformations and explore the set of all linear transformations from V to W. Challenge yourself with questions on linear transformations and their properties.
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