What am I doing wrong I am using the Gauss Jordan method to calculate this answer and some other students are coming up with differant answers.
Problem is
3x+y+z=5,
x+5y-z=-8,
10x+7y+z=2
My answer is (-6z+3,7z-4
_________, z
( 11 11)
Where I have +3 they have +33 and where I have -4 they have -44 Can you let me know how they came up with the larger numbers
This does not make sense to me. You have three equations, three unknowns. YOu can solve for x,y,z. Whatever you are doing, I don't understand.
What am I doing wrong I am using the Gauss Jordan method to calculate this answer and some other students are coming up with differant answers.
Problem is
3x+y+z=5,
x+5y-z=-8,
10x+7y+z=2
Answers are
1-(-6z+3/11, 7z-4/11,z)
2-(-6z+33/11,7z-44/11)
I got #1 for my answer and some got #2 which one is right. Some got all kinds of numbers.
well, I didn't get anything like that, I got a specific number solution for x, y, and z.
When you say "calculate" and answer, that to me implies looking for a specific solution.
Here is a Gauss Jordan applet, check your work
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
My mistake New at this Question should be Use the Gauss-Jordn method to solve the system of equations.
well, both your 1) and 2) are NOT solutions. Solutions have specific values for x,y, and z.
It seems that you and your classmates are using the Gauss Jordan method to solve a system of linear equations, but you're getting different solutions. The Gauss Jordan method is an algorithm that involves performing row operations on an augmented matrix to bring it into row-echelon form and then further manipulation to obtain the reduced row-echelon form.
To determine how your classmates are getting different answers with larger numbers, I will explain the steps involved in the Gauss Jordan method and provide a possible explanation for the discrepancy.
1. Write the augmented matrix: Start by writing the coefficients and constants of the system of equations in matrix form. In this case, the augmented matrix would be:
[ 3 1 1 | 5 ]
[ 1 5 -1 | -8 ]
[ 10 7 1 | 2 ]
2. Perform row operations: The Gauss Jordan method involves performing row operations to simplify the matrix.
a. Row switching: Swap rows to ensure that the top left element is not zero. If necessary, you can swap rows 1 and 3.
[ 10 7 1 | 2 ] [ 1 5 -1 | -8 ]
[ 1 5 -1 | -8 ] --> [ 3 1 1 | 5 ]
[ 3 1 1 | 5 ] [ 10 7 1 | 2 ]
b. Row scaling: Multiply a row by a scalar to create a leading one. Divide row 1 by 10.
[ 1 7/10 1/10 | 1/5 ]
[ 3 1 1 | 5 ]
[ 10 7 1 | 2 ]
c. Row replacement: Subtract suitable multiples of one row from other rows to create zeros below the leading one.
- Multiply row 1 by -3 and add it to row 2.
- Multiply row 1 by -10 and add it to row 3.
[ 1 7/10 1/10 | 1/5 ]
[ 0 17/10 -13/10 | 23/5 ]
[ 0 0 -17/10 | -1/2 ]
d. Row scaling (again): Multiply rows 2 and 3 by suitable scalars to create leading ones.
[ 1 7/10 1/10 | 1/5 ]
[ 0 1 -13/17 | 23/17 ]
[ 0 0 1 | 10/17 ]
e. Row replacement (again): Subtract suitable multiples of rows from other rows to create zeros above and below the leading ones.
- Multiply row 2 by -7/10 and add it to row 1.
- Multiply row 2 by -1/10 and add it to row 3.
[ 1 0 0 | 3 ]
[ 0 1 -13/17 | 23/17 ]
[ 0 0 1 | 10/17 ]
3. Interpret the solution: When the augmented matrix is in reduced row-echelon form, the rightmost column represents the values for the variables. In this case, it indicates that x = 3, y = 23/17 - 13/17z, and z = 10/17.
Now, the discrepancy in the numbers you mentioned (+3 vs. +33 and -4 vs. -44) could be due to calculation errors made by your classmates during the row operations. It's possible that they made mistakes while multiplying or adding the rows. I would recommend double-checking each step of the calculations to identify any errors. Even a small mistake in one row operation can lead to significant discrepancies in the final solution.
In summary, to ensure consistency in solutions, it is essential to pay close attention to the row operations performed in the Gauss Jordan method and be careful with calculations.