What is gauss eliminating method?

Answer 1

Consider a system of linear equations . Let be its coefficient matrix. elementary row operation.

(i) R(i, j): Interchange of the ith and jth row.

(ii) R(ci): Multiplying the ith row by a non-zero scalar c.

(iii) R(i, cj): Adding c times the jth row to the ith row.

It is clear that performing elementary row operations on the matrix (or on the equations themselves) does not affect the solutions. Two matrices and are said to be row equivalent if and only if one of them can be obtained from the other by performing a sequence of elementary row operations. A matrix is said to be in row echelon form the following conditions are satisfied:

(i) The number of first consecutive zerosincreases down the rows.

(ii) The first non-zero element in each row is 1.

The process of performing a sequence of elementary row operations on a system of equations so that the coefficient matrix reduces to row echelon form is called Gauss elimination. When a system of linear equations is transformed using elementary row operations so the coefficient matrix is in row echelon form, the solution is easily obtained by back substitution.