Geometric transformations with matrix multiplication

The  exercise appears under the Precalculus Math Mission. This exercise plays with matrices as representations of geometric transformations, rigid and dilations.

Types of Problems
There are three types of problems in this exercise:


 * 1) Select the options that are true about the matrix: This problem provides a matrix and several statements. The student is asked to select which of the options are true about the given matrix.Gtwmm1.png
 * 2) Give the matrix that represents the transformation: This problem shows a picture that has a transformation performed. The student is asked to write an appropriate matrix to represent the transformation in the diagram.Gtwmm2.png
 * 3) Tell which diagram represents the transformation: This problem provides a matrix and a selection of pictures of transformations. The student is expected to select the picture that represents the transformation in the matrix.Gtwmm3.png

Strategies
Knowledge of the matrix representation of geometric transformations is encouraged to ensure success on this exercise.
 * 1) A matrix of the form (a,0,0,a) is a dilation by a factor of a.
 * 2) A matrix of the form (cos,sin,-sin,cos) represents a rotation about the origin.
 * 3) Translations are not easily represented in matrices because they are not linear transformations (they do not send zero to zero).
 * 4) The reflection matrices are representable in matrices.

Real-life Applications

 * 1) Matrices are the foundational concept in linear algebra.
 * 2) Matrices can be a method for efficiently solving systems of linear equations.
 * 3) Matrices can be viewed as an extension of a number system.