Polynomial of Degree 2 through Given Points

In summary, to find the polynomial of degree 2 that goes through the points (1,-1), (2,3), and (3,13), you need to use the equation a*x^2+b*x+c=y and substitute the points to get three linear equations. Then, solve the system using the section on AX = 0 and homogeneous trivial solutions. It is likely that this question is covered in that section. You can try solving it by making it in rref.
  • #1
frasifrasi
276
0
Linear Algebra Question...

So, the professor assigned this problem even though the book never touches on it whatsoever. I have no clud how to do it, so I would appreciate if anyone can describe the process of demonstrate.

Q. Find the polynomial of degree 2 whose graph goes through points (1,-1), (2,3), and (3,13).

Thank you for the help!
 
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  • #2
A polynomial of degree 2 is a*x^2+b*x+c=y. Substitute your three points and you get three linear equation in the variables a,b,c. Solve the system.
 
  • #3
See the section where it talks about AX = 0, and about homogeneous trivial solutions (or non-trivial).
I strongly think that it would have something about this question in that section.
 
  • #4
Dick, I think you got it...I will try it.

Should I solve for it by making it in rref ?
 
Last edited:

FAQ: Polynomial of Degree 2 through Given Points

What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of vectors, matrices, and linear transformations. It involves the use of algebraic techniques to solve systems of linear equations and represent geometric concepts.

What is the difference between a vector and a matrix?

A vector is a quantity that has both magnitude and direction, and is typically represented by a column or row of numbers. A matrix is a rectangular array of numbers, and can be thought of as a collection of vectors. Vectors can be multiplied by scalars, while matrices can be multiplied by other matrices.

How is linear algebra used in real life?

Linear algebra has many applications in various fields, such as physics, engineering, computer graphics, and economics. It is used to solve systems of equations, analyze data sets, and model real-world situations.

What are eigenvectors and eigenvalues?

Eigenvectors are special vectors that, when multiplied by a matrix, produce a scalar multiple of themselves. Eigenvalues are the corresponding scalar multiples. They are used to analyze the behavior and transformations of a matrix.

Can linear algebra be used in machine learning?

Yes, linear algebra is an essential tool in machine learning. It is used to represent data and perform operations on it, such as dimensionality reduction, clustering, and regression. Many machine learning algorithms rely on linear algebra to make predictions and analyze data.

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