Prompt for creating articles in a mathematical direction.

Why not use ChatGPT? Here is what I got; note that the displayed text in ChatGPT is formatted better. I wish I could switch to markdown mode in this input box. @Hasan, would it be possible.

Kramer's method, also known as Cramer's Rule, is a mathematical algorithm used to solve systems of linear equations with as many equations as unknowns, ensuring a unique solution. This method is particularly useful for small systems and is based on the use of determinants. Here's a step-by-step guide to solving a system of linear equations using Cramer's Rule:

### Title: Solving Systems of Linear Equations Using Cramer's Rule

#### Introduction
Cramer's Rule is an elegant, determinant-based approach to solving systems of linear equations. This method is named after the Swiss mathematician Gabriel Cramer, who introduced the technique in 1750. It is applicable for systems where the number of equations matches the number of unknowns, and the system has a unique solution.

#### Understanding the Basics
A system of linear equations can be represented in matrix form as **Ax = b**, where **A** is a square matrix containing the coefficients of the variables, **x** is a column vector of the variables, and **b** is a column vector of the constants.

#### Prerequisites for Cramer's Rule
1. **Square Matrix:** The coefficient matrix **A** must be square (equal number of rows and columns).
2. **Non-zero Determinant:** The determinant of matrix **A** (denoted as det(A)) must be non-zero.

#### Steps in Cramer's Rule
1. **Determine the Determinant:** Calculate the determinant of the coefficient matrix **A**. If det(A) = 0, Cramer's Rule cannot be applied.
2. **Create Modified Matrices:** For each variable, create a modified matrix by replacing the column corresponding to that variable in **A** with the constant vector **b**.
3. **Calculate Determinants of Modified Matrices:** Find the determinants of these modified matrices.
4. **Solve for Variables:** Each variable is calculated by dividing the determinant of its modified matrix by det(A).

#### Example
Consider a system of two equations:

\[ a_1x + b_1y = e_1 \]
\[ a_2x + b_2y = e_2 \]

The coefficient matrix **A** and the constant vector **b** are:

\[ A = \begin{pmatrix} a_1 & b_1 \\ a_2 & b_2 \end{pmatrix}, \quad b = \begin{pmatrix} e_1 \\ e_2 \end{pmatrix} \]

To solve for x:
1. Replace the first column of **A** with **b**:
\[ A_x = \begin{pmatrix} e_1 & b_1 \\ e_2 & b_2 \end{pmatrix} \]
2. Calculate det(A_x) and divide by det(A).

To solve for y:
1. Replace the second column of **A** with **b**:
\[ A_y = \begin{pmatrix} a_1 & e_1 \\ a_2 & e_2 \end{pmatrix} \]
2. Calculate det(A_y) and divide by det(A).

#### Conclusion
Cramer's Rule provides a straightforward technique for solving systems of linear equations with unique solutions. While it is computationally intensive for large systems, it is ideal for smaller systems, offering a clear and concise solution method.

Hello SSAdvisor. You don't quite understand what I meant. I know the theory of the method. I am interested in information on creating chatgpt prompts for writing the best content, for example, on the topic of the Kramer Method.

@mathros if you need education on creating prompts then try the Premium Courses. Else give us what you've tried with ChatGPT and we might be able to help you improve it.

@ssadvisor Got it, thanks for the info

@mathros Did you try anything yet? Are you stuck somewhere?

General tips:

1. Pick the style that you wanna write with.

2. Start with the outline and split it into parts. Don't go for one shot for a full article. 

just try something and share your feedback, maybe we can help improve the results.

quản trị viên ơi tôi muốn học thêm nhiều về youtebe

@0965919923 English please. What is it you want to learn about YouTube? What have you tried?

@admin Hello. Here is an example of a ChatGPT prompt that I used to create an article on "Solving systems of linear equations using the Gaussian method":

You are an expert in numerical methods. You have more than 10 years of experience teaching students and students. Write me an article for the site on the topic "Solving systems of linear equations by the method of Gauss with the selection of the main element". The article reveals the following topics: Analysis of the method of Gauss with the selection of the main element: how to find the solution of systems of linear equations, Solution of systems of linear equations by the method of Gauss with the selection of the main element: a detailed description of the algorithm, Problems with calculating the solution of systems of linear equations by the Gaussian method with the selection of the main element: division by zero and their avoidance, and give examples with solutions. The article should contain 5000 words. Divide the article into sections and write an introduction

Of course, the result was not what I expected. I had to write each section myself, and then again try to edit it using ChatGPT

Posted by: @mathros

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Of course, the result was not what I expected. I had to write each section myself, and then again try to edit it using ChatGPT

Which version of ChatGPT were you using 3.5 or 4? 5000 words in one go is a bit of a stretch due to the token limitations. It's better to have GPT create an outline then continue by prompting it to expand the outline sections. If you have a paid subscription you could try using https://platform.openai.com/playground for more choices on the LLM that you can use giving a better result.

Posted by: @ssadvisor

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Which version of ChatGPT were you using 3.5 or 4?

Currently using the free version.

Posted by: @ssadvisor

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It's better to have GPT create an outline then continue by prompting it to expand the outline sections.

How do I formulate a prompt to get the structure?

@mathros see this comment https://learnwithhasan.com/forum/postid/1142/

@ssadvisor OK. Thank you