How to get the 4th equation using this data(lenear algebra)

  • Thread starter transgalactic
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In summary: I found a matrix A such that A*(u1-u2) = 0 and A*(u1-u3) = 0 and A*(u2-u3) = 0. I even said what the matrix A is.
  • #1
transgalactic
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this is the data that i was given about the question:
http://img23.imageshack.us/img23/6041/49022610ps1.th.gif

i need to find the matrix of T
i know that T is of 2X4 size
so i built T as
a1 a2 a3 a4
b1 b2 b3 b4

and multiplied by the given vector
i built a matrix for "a" parameters and "b" parameters
but i got only 3 equation instead of the needed 4
in order to get the values of "a"'s and "b"'s

how to use the independent vectors data to construct the 4th equation??
 
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  • #2
Let's call your vectors u1 = [1 1 0 1], u2 = [0 1 0 1], and u3 = [1 1 0 0].
Since Tu1 = Tu2 = Tu3 = [1 1], then
Tu1 - Tu2 = [0 0] ==> T(u1 - u2) = [0 0]
Tu1 - Tu3 = [0 0] ==> T(u1 - u3) = [0 0]
Tu2 - Tu3 = [0 0] ==> T(u2 - u3) = [0 0]

These equations tell us that u1 - u2, u1 - u3, and u2 - u3 are in the nullspace of T.
Find these vectors, and find a subset of them that is a linearly independent set. From those vectors you can get values for the entries of the matrix corresponding to the transformation T.
 
  • #3
i solved it differently
i said
T=(a1 a2 a3 a4)
(b1 b2 b3 b4)

and built an equations T*U1=(1,1) T*U2=(1,1) T*U3=(1,1)
so i get for "a" parameters only 3 equations
which is not enough
how to use the data that those vectors are independant
in order to build the 4th "a" parameter equation

( the same thing goes for "b" parameters)

??
 
Last edited:
  • #4
You say you solved it differently, but you're still asking questions, so it doesn't sound like the problem is actually solved. On the other hand, I actually found a matrix A for which A*u1 = [1 1], A*u2 = [1 1] and A*u3 = [1 1], so which is the better solution?
 
  • #5
you are not using he fact that two vectors are independent
??
 
  • #6
Yes, I am. Look at what I said in post #2.
 

1. How do I determine which data points to use for the 4th equation?

The data points used for the 4th equation should be chosen based on the specific problem you are trying to solve. Look at the relationships between the variables and consider which data points would best represent those relationships.

2. Can I use any linear algebra method to find the 4th equation?

Yes, there are several linear algebra methods that can be used to find the 4th equation, such as Gaussian elimination, matrix inversion, or using the least squares method. The method you choose will depend on the specific data and problem at hand.

3. What if my data does not fit a linear model?

If your data does not fit a linear model, you may need to consider other types of equations, such as polynomial or exponential models. Linear algebra methods can still be used to find the best fit for these types of equations as well.

4. How many data points do I need to find the 4th equation?

The number of data points needed to find the 4th equation will depend on the number of variables in the equation. In general, at least 4 data points are needed for a linear equation with 2 variables, and at least 3 data points are needed for a linear equation with 3 variables.

5. Can I use a calculator or computer program to find the 4th equation?

Yes, there are many calculators and computer programs available that can perform linear algebra calculations and find the 4th equation using data. However, it is important to understand the steps and concepts behind these methods in order to properly interpret and use the results.

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