**Gauss Jordan Elimination Method Examples**. Add times the equation to the equation (or ). Examples of sections 2.5 question 1.

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Example 2 (cont.) if f 3 2f 2 f 1 = 0. then x 3 can be chosen arbitrarily and x 2;x 1 can be determined by backsubstitution. X 1 = (f 1 3x 2+2x 3)=2: Using gauss elimination method. solve:

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There are three elementary row operations used to achieve reduced row echelon form: If f 3 2f 2 f 1 = 0. then x 3 = any scalar;

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Write the system as an augmented matrix. Consider the $m\times n$ system of linear equations:

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X + y + z = 9. 2y + z = 4 x + y + 2z = 6 2x + y + z = 7 output :

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The student then performs the same process in column 2. but first a 1 is established in position a The augmented matrix of the system is the following.

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A_{2 1} x_1+a_{2 2}x_2+\cdots+a_{2 n}x_n =b_2 \\. Multiply the equation by (or ).

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There is a similar procedure known as gausselimination . in which row operations are carried out until the left part of the augmented matrix is in upper triangular form. X 2 = (f 2 f 1=2 4x 3)( 2=7);

#### Input The Pair (B 0;S 0) To The Forward Phase. Step (1).

This form is characterized by 1’s on the diagonal. 0’s above and below the diagonal on the left side of the vertical line. and any numbers on the right. 1 1 1 5 2 3 5 8 4 0 5 2 we will now perform row operations until we obtain a matrix in reduced row echelon form. \begin{align*} a_{1 1} x_1+a_{1 2}x_2+\cdots+a_{1 n}x_n =b_1 \\.

#### Multiply The Equation By (Or ).

There are three elementary row operations used to achieve reduced row echelon form: A = [ 2 6 − 2 1 6 − 4 − 1 4 9]. Perform the given row operations in succession on the matrix.

#### The Last Equation Gives The Second Equation Now Gives Finally The First Equation Gives Hence The Set Of Solutions Is A Unique Solution.

Examples of gaussian elimination example 1: Look at the rst entry in the rst row. X + y + z = 9.

#### Solve The Following Linear System Using Gaussian Elimination Method.

It is really a continuation of gaussian elimination. X + 3y + 2z = 2 2x + 7y + 7z = −1 2x + 5y + 2z = 7 (this is the same system given as example of section 2.1 and 2.2; Final augmented matrix is :

#### Compare The Method Used Here With The One Previously Employed).

X+y +z = 5 2x+3y +5z = 8 4x+5z = 2 solution: Solve system of equations with 3 variables. A_{2 1} x_1+a_{2 2}x_2+\cdots+a_{2 n}x_n =b_2 \\.