Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the role of the scalar K in matrix dilation?

1. It defines the number of dimensions

2. It adjusts the angle of rotation

3. It scales all matrix values uniformly

4. It specifies the type of reflection

The correct answer is: It scales all matrix values uniformly

In the context of matrix dilation, the scalar K plays a crucial role by determining the uniform scaling of the matrix values. When multiplying a matrix by a scalar, each entry in the matrix is multiplied by that scalar K. This operation effectively enlarges or shrinks the matrix geometrically; when K is greater than one, the matrix is dilated or enlarged, making any geometric shape represented by the matrix bigger. Conversely, when K is a fraction between 0 and 1, the matrix contracts, reducing the size of the shape represented. Thus, the scalar K directly influences the size of the transformations without altering the relative proportions or the angles between vectors in the matrix, hence preserving the shape's structure. This uniform scaling is essential in various applications, such as in graphics transformation, where objects may need to be resized while maintaining their shape.