Linear Transformations Quiz

The image of a vector under a linear transformation lies in:

• The domain

• The null space

• The codomain

• The kernel

The zero transformation maps:

• Each vector to itself

• Each vector to the zero vector

• Only the zero vector to zero

• Vectors to their additive inverses

A linear transformation is completely determined by:

• Its range

• Its null space

• Its action on a basis of the domain

• Its matrix inverse

The null space of a linear transformation is:

• The set of all images

• The set of all vectors mapped to zero

• The set of all basis vectors

• The domain of the transformation

A linear transformation is said to be injective (one-to-one) if:

• Every input has a unique output

• Its null space is trivial

• The range is the entire codomain

• It is not invertible

A transformation is surjective if:

• Every output has a unique input

• It has a non-trivial kernel

• Every element of the codomain is in the range

• It is not linear

The matrix representation of a linear transformation depends on:

• The function definition only

• The domain and codomain

• The choice of basis

• The nullity of the transformation

The columns of the matrix of a linear transformation TT correspond to:

• The images of the basis vectors

• The range space

• The eigenvalues

• The null space basis

The standard matrix of a linear transformation T(x)=Ax is:

• The identity matrix

• The matrix A itself

• The inverse of A

• The transpose of A

If T is represented by matrix A, then the range of T is:

• The null space of A

• The column space of A

• The row space of A

• The diagonal of A