Gauss-jordan 3 equation matrix help

  • Thread starter bdh2991
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  • #1
bdh2991
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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?
 

Answers and Replies

  • #2
36,652
8,652

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.
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
bdh2991
103
0
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
36,652
8,652
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.
, 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
bdh2991
103
0
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?
 
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