Problem in setting homogenous parameters

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In summary, the equations x+z=0 and y-z+2w=0 can be rewritten as x=(1,0,-1,-.5)y and y=(0,1,0,-.5)y, where y is a vector containing two parameters. These equations can be used to find two vectors that form a basis for the nullspace of the matrix A.
  • #1
shellizle
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Homework Statement



how to put x+z=0, and y-z+2w=0 into matrices in terms of two parameters?


Homework Equations


AX=0, looking for x


The Attempt at a Solution



x=-z
y=z-2w

(-1, 1, 1, 0)z, no idea what the other matrix is :S

thanks advance guys!
 
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  • #2
Your question is somewhat misleading. I don't think you want to put the equations into matrices, but rather find two vectors that are a basis for the nullspace (or kernel) of your matrix A.

You can write z and w in terms of x and y, like so:
z = -x
w= -.5x -.5y
In the latter equation, I substituted -x for z in the equation y -z + 2w=0.


x=1x+0y
y=0x+1y
z=-1x+0y
w=-.5x-.5y

So in the equations above, a vector x = (x, y, z, w) can be written as a linear combination of two other vectors.
 

FAQ: Problem in setting homogenous parameters

What is a homogenous parameter?

A homogenous parameter is a variable that has the same value or characteristics across different groups or samples. In other words, it is a parameter that is consistent and does not vary significantly across a given population or dataset.

Why is setting homogenous parameters important?

Setting homogenous parameters is important because it allows for accurate and fair comparisons between different groups or samples. It helps to eliminate confounding variables and ensures that any observed differences are due to the independent variable being studied and not other factors.

What challenges may arise when trying to set homogenous parameters?

Some challenges that may arise when trying to set homogenous parameters include collecting accurate and consistent data, identifying all relevant variables, and accounting for potential confounding factors. It may also be difficult to find a perfect balance between making parameters too broad and too narrow.

How can one address the issue of heterogeneity in a dataset?

To address the issue of heterogeneity in a dataset, one can use statistical techniques such as stratification or matching to control for confounding variables and create more homogenous groups. Additionally, careful data collection and thorough analysis can help to identify and account for any potential sources of heterogeneity.

Are there any limitations to setting homogenous parameters?

Yes, there are some limitations to setting homogenous parameters. In some cases, it may be difficult or impossible to control for all variables and create truly homogenous groups. Additionally, the process of setting homogenous parameters may be time-consuming and costly. It is also important to consider the potential impact of homogenization on the generalizability of findings to the larger population.

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