# High-order determinants: easier way?

• Mego05
In summary, the speaker has successfully found a method for finding determinants of any order through expansion of minors and has also written a C++ program to do so. However, they are looking for a simpler method for finding determinants of 4th-10th order, as the current method is becoming tiresome. They have searched for 'determinant algorithms' but have only found information on eigenvalues, pivoting, and vectors, which they do not understand. They are a sophomore in high school and currently only familiar with determinants for use in Cramer's Rule.

#### Mego05

Ok, so I understand the method of finding a determinant of any order by expansion of minors. I was recently challenged by my teacher to find the determinant of a 10th order determinant she gave me. I succeeded, and felt quite proud of myself, after working for 3 months and filling up 300 pages with the math. Recently, I have grown fond of programming, and challenged myself to write a program in C++ that will find any determinant of an order of 10 or less. Coding the basic algorithm for expansion of minors has become quite tiresome. So, I am wondering, is there a simpler way to find any determinant? I'm only concerned with 4th-10th order determinants, as 2nd and 3rd orders are relatively painless. The solution has to be universal.

I'm not worried about implementing the method, as I can figure that out on my own. I just want to know if there is a simpler way (simpler here meaning needing less than 250,460 minors, and minors of minors, and so on) to go about finding a determinant?

Have you tried searching for 'determinant algorithms'?

I have, but everything I've found talks about eigenvalues, pivoting, and vectors. I have absolutely no idea what any of those are. Please take into account that I am a sophomore in high school, currently enrolled in an Algebra II class that covered determinants only for use in Cramer's Rule.

## 1. What are high-order determinants?

High-order determinants refer to matrices with dimensions higher than 2x2. In other words, they are matrices with more than two rows and columns.

## 2. What makes high-order determinants difficult to calculate?

The larger the dimensions of a matrix, the more complex the calculations become. High-order determinants involve a larger number of multiplications and additions, making them more time-consuming and prone to errors.

## 3. Is there an easier way to solve high-order determinants?

Yes, there are various methods and techniques that can make solving high-order determinants easier. These include using row operations, expanding by minors, and using Cramer's rule.

## 4. Can high-order determinants be solved by hand?

Yes, high-order determinants can be solved by hand, although they may be time-consuming and prone to errors. Using a calculator or computer program can make the process faster and more accurate.

## 5. How are high-order determinants used in science?

High-order determinants are used in various scientific fields, such as physics, engineering, and statistics. They are used to solve systems of equations, calculate areas and volumes, and analyze data. They are also used in applications such as computer graphics and cryptography.