Podcast
Questions and Answers
Which of the following statements is true about linear transformations?
Which of the following statements is true about linear transformations?
- Linear transformations can only have one domain.
- Linear transformations must be linear maps.
- Linear transformations can be nonlinear maps. (correct)
- Linear transformations can only have one codomain.
What is the definition of linear independence?
What is the definition of linear independence?
- The set of vectors is linearly independent if the equation Ax = b has a unique solution.
- The set of vectors is linearly independent if the only solution to the equation Ax = 0 is the trivial solution. (correct)
- The set of vectors is linearly independent if the equation Ax = 0 has no solutions.
- The set of vectors is linearly independent if the equation Ax = 0 has infinitely many solutions.
What is the range of a linear transformation T?
What is the range of a linear transformation T?
- The set of all possible inputs of T.
- The set of all possible solutions to the equation T(x) = 0.
- The set of all possible outputs of T. (correct)
- The set of all possible solutions to the equation T(x) = b.
What is the definition of a basis?
What is the definition of a basis?
What is the difference between linear transformations and linear maps?
What is the difference between linear transformations and linear maps?
What is the definition of linear dependence?
What is the definition of linear dependence?
What is the range of a linear transformation with a domain of dimension d?
What is the range of a linear transformation with a domain of dimension d?
What is the difference between a basis and a linear transformation?
What is the difference between a basis and a linear transformation?
What is the codomain of a linear transformation?
What is the codomain of a linear transformation?
What is the difference between a linear transformation and a linear map?
What is the difference between a linear transformation and a linear map?