Systems of Linear Equations
Consider system of m linear equations with n unknowns:
(2)
Definition. The numbers are called a solution of system (2) if substituting them into the equations, we obtain true equalities.
Definition. A system of equations (2) is said to be consistent if it has at least one solution, and it is said to be inconsistent if it has no solutions.
Definition. A system is called determined if it has a unique solution, and it is called undetermined if it has many solutions.
For example, the system of equations
has no solutions, i.e., it is inconsistent, because its lefthand sides are equal, while the righthand sides are different.
is consistent, but undetermined, because it has infinitely many solutions. Reducing the second equation by 3, we obtain two identical equations.
Consider the following system of n linear equations with n unknowns
(3)
It is required to find a solution of system (3), expressed in terms of the coefficients and the free terms , where (from 1 to n).
Date: 20150102; view: 954
