3. Introduction CONCEPT OF SYSTEM OF LINEAR EQUATIONS. System of m equations with n unknowns. It is a set of algebraic expressions of the form xj, are the unknowns , (j = 1,2 ,..., n). aij, are the coefficients (i = 1,2 ,..., m) (j = 1,2 ,..., n). ci, are independent terms, (i = 1,2 ,..., m).
9. which are the Cramer formulas, which are reflected in the following rule: Cramer's rule. The value of the unknown in a system xj Cramer is a fraction whose numerator is a determining which ob is to replace the column by the column j are the independent terms, and whose denominator is * A *.
10. Example Solve the system: Then, Cramer is a system. Therefore, the solution of the system is Solve the system: Then, Cramer is a system. Therefore, the solution of the system is:
13. Solving the equations, beginning with the last is: This is a compatible system determined . Solve the system: The augmented matrix is, Exchanging the first row with the third is: Then, the system has been as follows: Solving the last equation, z = 1 +2 t; if we do t = ", is: z = 1 +2
14. System solutions are giving arbitrary values to the parameter. " It is a compatible system undetermined. Solve the system: The augmented matrix is, We exchanged the first two rows is: After the system has been as follows: It is noted that the system is incompatible.
15.
16. The following algorithm performs the TDMA, overwriting the original arrays. In some situations this is not desirable, so some prefer to copy the original arrays beforehand. Forward elimination phase For k = 2 step until n do
