Arr Lin. algebra problem (frustrating)

  • Thread starter georgeh
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In summary, the conversation discusses a transformation on polynomials represented by a given matrix [1,1;1,-1] and its corresponding coordinate vector and result. The solution manual provides the formula T(ax+b)=(a+b)x+(a-b) for the transformation, but the speaker does not understand how it was derived. They also mention the use of the symbols \epsilon and P_1(\mathbb{R}), but there is confusion with their display. Further clarification is needed on the example and its corresponding element in P_1(\mathbb{R}).
  • #1
georgeh
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the question asks;
Consider the following matrices. What is the corresponding transfrmation on polynomials? Indicate the domain P_i and the codomain p_j
The matrix is: [1,1;1,-1]
I looked at the sol. manual and it states
T(ax+b)=(a+b)x+(a-b)
I seriously have no idea how they came up with that. I read the section and i don't see any examples on how to do it.
 
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  • #2
Given an arbitrary polynomial [itex]ax+b \epsilon P_1(\mathbb{R})[/itex], what is its coordinate vector with respect to the standard ordered basis for [itex]P_1(\mathbb{R})[/itex]?

What is the result when you multiply this coordinate vector (on the left) by your matrix?

What is the element of [itex]P_1(\mathbb{R})[/itex] that corresponds to this result?
 
Last edited:
  • #3
the first line should be [itex]ax+b \ \epsilon \ P_1(\mathbb{R})[/itex]. For some reason the symbol [itex]\epsilon[/itex] isn't showing.
 

1. What is Arr Lin. algebra problem?

Arr Lin. algebra problem, short for "arrangement linear algebra problem", is a type of mathematical problem that involves finding the number of ways to arrange a set of objects or variables in a specific order or pattern. It is commonly encountered in combinatorics and discrete mathematics.

2. Why is Arr Lin. algebra problem considered frustrating?

Arr Lin. algebra problem can be frustrating because it often involves complex calculations and requires a deep understanding of mathematical concepts. Additionally, there may be multiple steps and approaches to solving the problem, making it challenging to find the most efficient solution.

3. How do you solve an Arr Lin. algebra problem?

To solve an Arr Lin. algebra problem, you first need to identify the type of arrangement or pattern being asked for. Then, you can use mathematical formulas or methods such as permutations, combinations, or the binomial theorem to calculate the number of possible arrangements. It is also important to carefully consider the given conditions and restrictions in the problem.

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One helpful tip for solving Arr Lin. algebra problems is to break down the problem into smaller, more manageable parts. This can help you better understand the problem and identify the most efficient approach to solving it. Additionally, it is important to practice and become familiar with various mathematical formulas and techniques commonly used in Arr Lin. algebra problems.

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Yes, Arr Lin. algebra problems can have real-world applications. For example, they can be used to calculate the number of possible outcomes in probability problems, to determine the number of seating arrangements at an event, or to analyze the possible combinations of ingredients in a recipe. Understanding Arr Lin. algebra can also be useful in fields such as computer science, economics, and physics.

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