Gauss-jordan 3 equation matrix help

  • Thread starter bdh2991
  • Start date
  • Tags
    Matrix
In summary, The original problem is a matrix with 3 rows and 4 columns. The problem solver got as far as a new matrix with one of the rows being incorrect. The book's solution is not entirely correct either. The problem solver used various row operations to try to solve the problem, but it was later discovered that there was a mistake in the original matrix. The problem solver also asked about the validity of dividing a row by itself as a row operation.
  • #1
bdh2991
103
0

Homework Statement



the original problem is in matrix form:

1 1 2 8
-1 -2 -3 1
3 -7 4 10

Homework Equations





The Attempt at a Solution



i got all the way to :

1 1 0 -4
0 1 0 1
0 0 1 2

however, the top row is supposed to = 3 but when i subtract row 2 from row 1 i get -5...i can't find where i messed up in the steps i did it. anyone get the same thing as me or know what i did wrong?
 
Physics news on Phys.org
  • #2
bdh2991 said:

Homework Statement



the original problem is in matrix form:

1 1 2 8
-1 -2 -3 1
3 -7 4 10

Homework Equations





The Attempt at a Solution



i got all the way to :

1 1 0 -4
0 1 0 1
0 0 1 2
I don't know what you did to get the matrix above, but it's incorrect. This says that y = 1 and z = 2. From these you can work back to get x.

In any case, these values are incorrect. I've worked through the row reduction, and have a solution, which I have checked, so I know it's right.

Can you show what work you did to get the above? From that, we can tell you where you went astray.
bdh2991 said:
however, the top row is supposed to = 3 but when i subtract row 2 from row 1 i get -5...i can't find where i messed up in the steps i did it. anyone get the same thing as me or know what i did wrong?
 
  • #3
Mark44 said:
I don't know what you did to get the matrix above, but it's incorrect. This says that y = 1 and z = 2. From these you can work back to get x.

In any case, these values are incorrect. I've worked through the row reduction, and have a solution, which I have checked, so I know it's right.

Can you show what work you did to get the above? From that, we can tell you where you went astray.

that's weird because the book answer says that x = 3, y = 1, and z = 2, which is why i thought i only got the top row part wrong. the operations i used were:

row 2 * -1 minus row 1

row 3 minus 3 * row 1

10 * row 2 + row 3

row 3 / -52

5 * row 3 plus row 2

2 * row 3 minus row 1

row 2 minus row 1
 
  • #4
bdh2991 said:
that's weird because the book answer says that x = 3, y = 1, and z = 2
That is not a solution to the problem you posted.
The augmented matrix you posted is
1 1 2 8
-1 -2 -3 1
3 -7 4 10

The book solution works in the 1st and 3rd equations, but it doesn't work in the 2nd equation.

-1(3) -2(1) -3(2) = -3 -2 -6 = -11 ≠ 1

There are a couple of possibilities. It might be that you mistyped the original matrix. If the 2nd row was actually -1 -2 -3 11, then the book's answer is correct.


Otherwise, the book's answer is wrong.
bdh2991 said:
, which is why i thought i only got the top row part wrong. the operations i used were:

row 2 * -1 minus row 1

row 3 minus 3 * row 1

10 * row 2 + row 3

row 3 / -52

5 * row 3 plus row 2

2 * row 3 minus row 1

row 2 minus row 1
 
  • #5
Mark44 said:
That is not a solution to the problem you posted.
The augmented matrix you posted is
1 1 2 8
-1 -2 -3 1
3 -7 4 10

The book solution works in the 1st and 3rd equations, but it doesn't work in the 2nd equation.

-1(3) -2(1) -3(2) = -3 -2 -6 = -11 ≠ 1

There are a couple of possibilities. It might be that you mistyped the original matrix. If the 2nd row was actually -1 -2 -3 11, then the book's answer is correct.Otherwise, the book's answer is wrong.
You are correct, i accidentally put a -3 in the second row when it should have been a 3. My apologies to everyone. Also, is it a valid row operation to divide a row by itself?
 
Last edited:

What is a Gauss-Jordan 3 equation matrix?

A Gauss-Jordan 3 equation matrix is a system of three linear equations with three variables that is represented in matrix form. This type of matrix is often used to solve systems of equations and find the values of the variables that satisfy all three equations simultaneously.

How do I solve a Gauss-Jordan 3 equation matrix?

To solve a Gauss-Jordan 3 equation matrix, you can use the Gauss-Jordan elimination method. This involves manipulating the matrix using a series of row operations until it is in reduced row-echelon form. The values of the variables can then be read directly from the matrix.

What are the benefits of using Gauss-Jordan 3 equation matrix?

Gauss-Jordan 3 equation matrix is a powerful mathematical tool that can be used to solve systems of equations quickly and accurately. It is also useful for solving problems with three unknown variables, which can be difficult to solve using other methods.

What are the limitations of Gauss-Jordan 3 equation matrix?

One limitation of Gauss-Jordan 3 equation matrix is that it can only be used to solve systems of linear equations. It also requires a certain level of mathematical knowledge and may be difficult for those without a strong background in algebra.

Are there any tips for successfully using Gauss-Jordan 3 equation matrix?

Some tips for successfully using Gauss-Jordan 3 equation matrix include making sure the matrix is set up correctly, keeping track of your row operations, and being careful to avoid mistakes when performing calculations. It can also be helpful to practice with simpler matrices before tackling more complex ones.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
263
  • Calculus and Beyond Homework Help
Replies
1
Views
613
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
194
  • Calculus and Beyond Homework Help
Replies
3
Views
220
  • Calculus and Beyond Homework Help
Replies
2
Views
926
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
849
  • Calculus and Beyond Homework Help
Replies
3
Views
512
Back
Top