# Linear Algebra Discipline

Since the sum of moments on the left of each balance equals the sum of moments on the right (the moment of an object is it is mass times its distance from the balance point), the two balances give this system of two equations (Hefferon).

The second example of a linear system is from Chemistry. We can mix, under controlled conditions, toluene C7H8 and nitric acid HNO3 to produce trinitrotoluene C7H5O6N3 along with the byproduct water (conditions have to be controlled very well, indeed-trinitrotoluene is better known as TNT). In what proportion should those components be mixed

Our next example is about solving a riddle. There are two groups of people X and Y having a certain number of persons in each group. If a person from X leaves to join Y then Y becomes double of X. If a person leaves Y to join X then they both become equal to each other. How many persons are there in each group

The objective is to determine if such a system of linear equations has a solution or not. That is to find out if there exist values of x1 to xn which when fed into this equation will simultaneously satisfy all the equations. If true then the system is said to be consistent or else it is inconsistent (Matthews).

The matrix is called the coefficient matrix of the system of equations as it only has the coefficients of variables listed in it. If this matrix were also to include the constants involved in the equations then it would be called an augmented matrix of the system and. .

Three elementary row operations can be performed on matrices which do not affect the solution of linear equations.

1. Interchanging two rows

2. Multiplying a row by a non-zero number

3. Adding a multiple of one row to another .