Converting equations into vectores

  • Thread starter Jalo
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In summary: So if we have the polynomial x2 + 3x + 1, we can represent it as 1(1) + 3(x) + 1(x2). This can then be written as the vector (1, 3, 1). In summary, you can convert a polynomial equation into a vector by representing it as a linear combination of basis functions, with the coefficients of each basis function corresponding to the coordinates of the vector.
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Jalo
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Homework Statement



How do I convert a polinomial equation into a vector? Example:

x^2 + 3x + 1 How do I convert it into a vector like (x,y,z) (with as many variables as possible

Homework Equations





The Attempt at a Solution



The only thing I could remember was to isolate each x into a different vector, but I'm pretty sure I learned to do it in a better way at class, just don't remember it

x^2(1,0,0) + x(0,3,0 + (0,0,1)

Thanks ahead
 
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  • #2
Jalo said:

Homework Statement



How do I convert a polinomial equation into a vector? Example:

x^2 + 3x + 1 How do I convert it into a vector like (x,y,z) (with as many variables as possible

Homework Equations





The Attempt at a Solution



The only thing I could remember was to isolate each x into a different vector, but I'm pretty sure I learned to do it in a better way at class, just don't remember it

x^2(1,0,0) + x(0,3,0 + (0,0,1)

Thanks ahead

I'm guessing that you are working with function spaces, which are similar to vector spaces. In a vector space, the coordinates of a given vector indicate a particular linear combination of basis vectors. For example, in R3, the standard basis is e1 = <1, 0, 0>, e2 = <0, 1, 0>, and e3 = <0, 0, 1>.

The vector <3, -1, 2> = 3e1 + (-1)e2 + 2e3.

In the function space of polynomials of degree 2 or less (P2), one basis is the set of functions {1, x, x2}. You can represent any polynomial of degree two or less as a linear combination of these basis functions.
 

1. How do I convert an equation into a vector?

To convert an equation into a vector, you need to identify the variables in the equation and represent each variable as a coordinate in the vector. For example, if your equation is y = mx + b, your vector would be represented as (x, y).

2. What is the purpose of converting equations into vectors?

The purpose of converting equations into vectors is to simplify complex equations and make them easier to work with. Vectors also allow us to visualize and manipulate mathematical concepts in a geometric way.

3. Can all equations be converted into vectors?

No, not all equations can be converted into vectors. Generally, equations that involve multiple variables and operations such as multiplication and division are more suitable for vector representation. Simple linear equations are the easiest to convert into vectors.

4. How can converting equations into vectors be useful in real-life applications?

In real-life applications, converting equations into vectors is useful for solving problems in fields like physics, engineering, and computer science. Vectors can represent physical quantities, such as force and velocity, and can be used to model and analyze real-world situations.

5. Are there any limitations to converting equations into vectors?

Yes, there are some limitations to converting equations into vectors. Vectors cannot represent equations with complex mathematical operations or equations with infinite solutions. Additionally, vectors are limited to representing equations in two or three dimensions, so they may not always be applicable in higher dimensions.

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