use gauss jordan elimination method tofind solution set of4x+5y+3z=23.3x+2y+z=10.2x+5y-z=9
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gauss jordan elimination method online
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Gaussian elimination calculator - OnlineMSchool
When page be open type your coefficients and click option Solve the system.
You will see solution step-by step.
Of course in the sollutions replace:
x1 with x , x2 with y and x3 with z
On this site you can practice gauss jordan elimination method.
To find the solution set using the Gauss-Jordan elimination method, we need to perform row operations on the augmented matrix of the given system of equations. Let's begin:
Step 1: Write the augmented matrix
The augmented matrix for the system of equations is:
[ 4 5 3 | 23 ]
[ 3 2 1 | 10 ]
[ 2 5 -1 | 9 ]
Step 2: Perform row operations to transform the augmented matrix into row-echelon form
1. Multiply Row 1 by 1/4 to get a leading coefficient of 1 in the first equation:
[ 1 5/4 3/4 | 23/4 ]
[ 3 2 1 | 10 ]
[ 2 5 -1 | 9 ]
2. Multiply Row 1 by -3 and add it to Row 2, multiply Row 1 by -2 and add it to Row 3 to eliminate the first column entries below the leading coefficient:
[ 1 5/4 3/4 | 23/4 ]
[ 0 -7/4 -7/4 | -5/4 ]
[ 0 3/2 5/2 | 13/2 ]
3. Multiply Row 2 by -4/7 to get a leading coefficient of 1 in the second equation:
[ 1 5/4 3/4 | 23/4 ]
[ 0 1 1 | 5/7 ]
[ 0 3/2 5/2 | 13/2 ]
4. Multiply Row 2 by -5/4 and add it to Row 1, multiply Row 2 by -3/2 and add it to Row 3 to eliminate the second column entries below the leading coefficient:
[ 1 0 -1 | 11/7 ]
[ 0 1 1 | 5/7 ]
[ 0 0 1/2 | 13/14 ]
Step 3: Perform row operations to transform the augmented matrix into reduced row-echelon form
1. Multiply Row 3 by 2 to get a leading coefficient of 1 in the third equation:
[ 1 0 -1 | 11/7 ]
[ 0 1 1 | 5/7 ]
[ 0 0 1 | 13/14 ]
2. Multiply Row 3 by 1 and add it to Row 1, multiply Row 3 by -1 and add it to Row 2 to eliminate the third column entries above the leading coefficient:
[ 1 0 0 | 23/14 ]
[ 0 1 0 | 3/14 ]
[ 0 0 1 | 13/14 ]
Step 4: Read off the solution set
From the reduced row-echelon form, we can conclude that the solution set of the system of equations is:
x = 23/14
y = 3/14
z = 13/14
Therefore, the solution set is {(23/14, 3/14, 13/14)}.