TABLE OF CONTENTS Matrix and vector operations have wide applications in everyday engineering problems, yet the courses offered at the college and university level have become too abstract. Thus many students struggle with the abstract concepts, and seldom have opportunities to apply them to problem solving.
We know how to solve a set of simultaneous linear equations by Cramer's rule but when the dimension of the equations gets larger, a pencil and paper is far from adequate, and a solution by computer algorithm is in order.
Commercially available software packages at the elementary, intermediate, and advanced levels continue to grow in sophistication; however, students and engineers learn how to use these convenient tools but not how to construct a solution algorithm.
We give a quick review on the solutions of a set of simultaneous linear equations by Gaussian elimination with backsubstitution and forward substitution and rapidly culminate to a construction of matrix header file. The header file contains almost all the matrix operations required in engineering and general science problems.
We do not claim that our matrix header file is encyclopedic; however, it is more than adequate for the matrix operations covered in this textbook.
An example of a set of simultaneous linear equations is given below.
where a ij and b i are given
x i are unknown, to be solved.
Eq (1.1) can be written in a vector-matrix form,
A more compact form is,
We want to solve for the column vector
