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.