Question

Range of a linear transformation calculator.

A) Linear transformations have infinite ranges.
B) Range is determined by the coefficients of the linear transformation.
C) Multiply the input range by the transformation matrix.
D) Range is the set of all possible output values.

Answer 1

The range of a linear transformation is the set of all possible output values.

Step-by-step explanation:

The correct answer is D) Range is the set of all possible output values.

A linear transformation maps elements from one vector space to another. The range of a linear transformation refers to the set of all possible output values that can be obtained by applying the transformation to elements from the input space.

For example, consider a linear transformation that doubles every element in a vector. The range of this transformation is the set of all possible doubled values. If the input range is [1, 2, 3], then the output range would be [2, 4, 6].