# Mathematical system | Mathematics homework help

The algebra and “mathematical system” assumption of matrices is engaging consequently it

resembles a combine of the way genuine aggregate interact (repetition and abstracted continue) with

the way vectors interact (abstracted continues and there’s an “extra” repetition: scalar

multiplication). In abstracted, matrices can too be interpreted to reproduce-exhibit linear

transformations of Cartesian n-space, so there’s another lamina of purport implicated. In this

task, you’ll do some basic investigation of matrices and their changes of the Cartesian

plane.

Requirements:

A. Construct and allot a order matrix by doing the following:

1. Create a 2x2 order matrix A that is incongruous from I.

2. Determine, showing all performance, the precipitation of top (3, 2) when it is rotated using the

linear change generated by the matrix A.

B. Construct and excite 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 particularize the fourth minute of a matrix that is not

invertible when three of the entries are given.

C. Excite 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 abstractedal methods of your

choosing.