The algebra and “mathematical system” theory of matrices is fascinating because it

The algebra and “mathematical system” theory of matrices is fascinating because it

resembles a blend of the way real numbers interact (multiplication and addition exist) with

the way vectors interact (addition exists and there’s an “extra” multiplication: scalar

multiplication). In addition, matrices can also be interpreted to represent linear

transformations of Cartesian n-space, so there’s another layer of meaning involved. In this

task, you’ll do some basic exploration of matrices and their transformations of the Cartesian

plane.

Requirements:

A. Construct and apply a rotation matrix by doing the following:

1. Create a 2x2 rotation matrix A that is different from I.

2. Determine, showing all work, the location of point (3, 2) when it is rotated using the

linear transformation generated by the matrix A.

B. Construct and analyze a matrix that is not invertible by doing the following:

1. Create a 2x2 matrix B that is not invertible.

2. Demonstrate that matrix B is not invertible.

3. Demonstrate, using B, how to determine the fourth entry of a matrix that is not

invertible when three of the entries are given.

C. Analyze the invertible matrix M = [2 6] by doing the following:

2 4

1. Demonstrate that matrix M is invertible by showing that it has a nonzero

determinant.

2. Demonstrate that matrix M is invertible by computing the inverse using the inverse

formula for 2x2 matrices.

3. Demonstrate that matrix M is invertible using two additional methods of your

choosing.