Programming Assignment 6: Linear Equation System Solver
This assignment is to design and implement a C++ project of matrices and vectors with class inheritance. The project has a basis class Matrix and two derived sub-classes class Vector and class SMatrix, representing vectors and square matrices as given in matrix.h, smatrix.h, and vector.h, respectively. Assume indices of rows and columns starting from 0. Create a project directory Assignment6_DXXXXXXX. Also, create a C++ project named assignment6_DXXXXXXX.dev to include header files matrix.h, smatrix.h, and vector.h and their implementation matrix.cpp, smatrix.cpp, and vector.cpp. Write an application program linear_equation_system_solver.cpp to implement a linear equation system solver. Place the project file, the header files, and the source code files in project directory Assignment6_DXXXXXXX.
A system of linear equations with n variables X0, X1, ..., and Xn-1 is a set of n linear equations:
a0,0X0 +a0,1 X1 +...+a0,n-2 Xn-2 +a0,n-1 Xn-1 =c0 a1,0X0 +a1,1 X1 +...+a1,n-2 Xn-2 +a1,n-1 Xn-1 =c1
...an-1,0 X0 + an-1,1 X1 + ... + an-1,n-2 Xn-1 + an-2,n-1 Xn-1 = cn-1
These n linear equations can be written as a matrix-vector equation AX=C, where A is the n × n coefficient matrix, X is the solution column vector of length n, and C is the constant column vector of length n, that
aa⋯aaXc a0,0 a0,1 ⋯ a0,n−2 a0,n−1 X0 c0
1,0 1,1 1,n−2 1,n−1 1 1 A= ⋮ ⋮ ⋱ ⋮ ⋮ ,X= ⋮ ,andC= ⋮ .
an−2,0 an−2,1 ⋯ an−2,n−2 an−2,n−1 X cn−2 an−1,0 an−1,1 ⋯ an−1,n−2 an−1,n−1 Xn−2 cn−1
of the i-th column by vector C and 0 ≤ i < n. Theiapplication program should perform the following steps:
The solution of the linear equation system is Xi = A , where Ai is matrix A with replacement A
a. Input n as the rank of the linear equation system, 0 < n ≤ 10,
b. Randomly generate elements of coefficient matrix A and constant vector C. The
values of these elements are between 0 and 1.0.
c. Print the coefficient matrix A, constant vector C, and the system of linear equations.
d. Solve the linear equation system to obtain the result of solution vector X.
e. Print the solution of the linear equation system, i.e., the result of solution vector X.
f. Verify solution of the linear equation system, i.e., compute AX-C and check whether
it is the zero vector, error tolerance to six digits after the decimal point.
Compress directory Assignment6_DXXXXXXX to obtain the compressed file Assignment6_DXXXXXXX.YYY, where YYY is zip, rar, or 7z. Write a report Report6_DXXXXXXX.pdf to explain the experience of programming and development of this assignment. Submit Assignment6_DXXXXXXX.YYY and Report6_DXXXXXXX.pdf to iLearn. The assignment is due by 23:59 pm, Wednesday, May 29, 2024.
Program execution example:
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