使用Maxtix解决 [ Linear Equations ](https://www.mathsisfun.com/algebra/systems-
linear-equations-matrices.html “Linear Equations Using Matrix”) 问题。
Problem Description
Vector and matrix are data structures that are widely used in data science
applications. In this assignment, you are required to implement them in
abstract data types (ADT) with Python class and to apply matrix operations to
solve systems of linear equations without using any Python libraries for
vector and matrix operations such as NumPy. Submissions that do not implement
the data structures in Python classes will fail the assignment. The minimal
amount of data and methods to be defined in each corresponding ADT are as
follows:
Not allowed to use libraries that Provide matrix operation
Class Vector
- Data
- vector - vector represented in a list
- size - number of elements in vector
- Methods
- add(aVector) - vector of aVector will be added to the vector of the current instance of Vector with the result being stored in a new instance of Vector. The new instance will be returned.
- length() - return the length of vector (a non-negative numeric value)
- dot_product(aVector) - dot product of vector of aVector and the current vector, which is a numeric value, will be returned.
Class Matrix:
- Data
- matrix - matrix represented in a list of lists
- row_nos - number of rows of the matrix
- col_nos - number of columns of the matrix
- Methods
- add(aMatrix) - matrix of aMatrix is added to the matrix of the current instance of Matrix with the result being stored in a new instance of Matrix. The new Matrix instance will be returned.
- isSquare() - test whether the matrix of the current instance of Matrix is a square matrix. A Boolean value will be returned.
- det() - return the determinant of the matrix of the current instance of Matrix which is a numeric value.
- transpose() - return the transpose of the matrix of the current instance of Matrix as a new Matrix instance.
- inverse() - return the inverse of the matrix of the current instance of Matrix as a new Matrix instance.
In addition to defining and demonstrating the working of the Vector and Matrix
classes, a brief discussion on the worst-case time complexity of each method
is to be included too. The submission must also include a case that uses the
Matrix class to solve a system of linear equations (3 equations).
Assignment Requirements
The program must be developed in Python classes. Special purpose Python
modules such as NumPy are not allowed to use. A report of no more than 10
pages (excluding any appendices) that describes the program design with
illustrations of the proper working of each class method and their time
complexities is needed. A full listing of program codes should be included in
an appendix.
Submission Requirements
Submit your Python program (in .py or .ipynb extension) which should be
properly commented, and the corresponding report to Moodle.
Grading will be based on solution correctness and completeness, the efficiency
of the submitted solution, and the quality of the documentation.
