but I don't understand how to get to this result.Gaussian elimination to solve a system of n equations for n unknowns requires n(n+1) / 2 divisions, (2n3 + 3n2 − 5n)/6 multiplications, and (2n3 + 3n2 − 5n)/6 subtractions,[4] for a total of approximately 2n3 / 3 operations. Thus it has arithmetic complexity of O(n3). However, the intermediate entries can grow exponentially large, so it has exponential bit complexity.
The maximum of arithmetic operations refers to the maximum number of mathematical operations that must be performed in order to complete a given calculation or problem. This includes addition, subtraction, multiplication, division, and any other relevant operations.
Knowing the maximum of arithmetic operations needed can help in determining the efficiency and complexity of a mathematical algorithm or problem. It can also help in optimizing the process and finding more efficient ways of solving the problem.
The maximum of arithmetic operations needed is calculated by analyzing the mathematical problem or algorithm and identifying the number of operations that must be performed at each step. These operations are then added to determine the total maximum number of operations needed.
It is possible to reduce the maximum of arithmetic operations needed by finding more efficient ways of solving the problem or by using mathematical shortcuts. However, in some cases, the maximum number of operations needed may be unavoidable.
The complexity of the problem, the number and type of variables involved, and the chosen method of solving the problem can all affect the maximum of arithmetic operations needed. Additionally, the efficiency of the algorithm or process used can also have an impact.