Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

4 linear equations

I originally thought up
these four equations
hoping they would only
meet at one point and
I could solve for it using
matrices, but down below
you can see my one
point of intersection may
have blown up to something
bigger than that.  Does
anyone know what this
bigger thing is called?  Is
the intersection bigger like
some 3-d space in 4-d, or
is it a plane in 4-d?  Or any
other interpretation is
certainly welcome...

w + 2x + 3y + 4z = 5
6w + 7x + 8y + 9z = 10
11w + 12x + 13y + 14z = 15
16w + 17x + 18y + 19z = 20

Any ideas welcome.
Your take on this
system of equations
would be very helpful to me!!

Last edited by John E. Franklin (2014-02-26 03:29:39)

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 4 linear equations

Hi;

Looks like you made a mistake in your work because your final answer is slightly off.

Did you take the determinant of that system?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: 4 linear equations

I'll check my work and also I didn't take the determinant.

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 4 linear equations

Tell me when you get the determinant.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: 4 linear equations

Do I ignore the constants on the right side of the equations and
just do a determinant of the 4x4 matrix:

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 4 linear equations

That matrix is the problem right there. It is singular. You can not invert it therefore the system will not have a unique solution. That is why your final answer is not the nice neat  one you expected.

You can prove it is singular in another way. The determinant is 0!

There is even a third way, notice that row 4 =row 3 + row 2 - row 1. This means that the rows are not linearly independent therefore the determinant will be 0 and the matrix singular.

Here is another way 2 x row3 = row2 + row4

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: 4 linear equations

Thanks a lot for the help!!!  I finally got the zero for the determinant!!  I did it by hand!!  It worked though.

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igloo myrtilles fourmis

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 4 linear equations

Pick an example to use Gaussian elimination on that does not have a determinant of 0. Then everything will work out nice and neat. Good luck and happy computing.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.