Engineering Mathematics Algebra: Linear and Polynomial Equations

Engineering mathematics algebra is a fundamental subject that is used in a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical. It is the study of systems of polynomial equations in many variables, which requires a good understanding of linear equations, quadratic equations, polynomials, systems of equations, and inequalities. In this article, we will discuss these subtopics in the field of engineering mathematics algebra.

1. Linear Equations: A linear equation is a mathematical equation that represents a straight line in a two- or-3-d graph. It is usually written in the form of y = f(x), where f(x) is a linear polynomial in x. Linear equations are solved by performing operations on the rows of the augmented matrix, which simplify it to a form from which the solution of the system can be ascertained by inspection.

2. Linear Systems of Equations: A system of linear equations is a set of simultaneous linear equations that have the form of a matrix equation. Gaussian Elimination is a method used to solve systems of linear equations. It involves performing certain operations on the rows of the augmented matrix that simplify it to a form from which the solution of the system can be ascertained by inspection

3. Polynomial Equations: A polynomial equation is a mathematical equation that involves variables and coefficients. It is usually written in the form of f(x) = 0, where f(x) is a polynomial in x. The Fundamental Theorem of Algebra is used to solve polynomial equations. It ascertained that a polynomial of degree d in one variable x can be written as a linear equation in the variable x - d, and the solutions of the polynomial equation can be found by solving the linear equation

4. Systems of Polynomial Equations: A system of polynomial equations is a set of simultaneous polynomial equations that have the form of a matrix equation. Solving systems of polynomial equations is a classical problem in mathematics. There are many methods for solving polynomial systems, such as continuation methods, numerical methods, and symbolic methods