# Solving 3x3 matrix

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Functional analysis is involved in both fields, which also shows that analysis and algebra are not mutually exclusive, and it is likely that the contents of both fields can be used to solve a certain problem..

What is the difficulty in solving problems with formula or model thinking? In the simple example of throwing stones to find the distance, the difficulty is not to solve the quadratic equation of one variable, but that your thinking ability can transform the problem in this business scenario into a problem of solving the company. After completing this transformation, all that remains is the process of matching using your formula library. You can think about how much education at the current school stage teaches students how to transform their thinking ability? More school learning often relies on a large number of question type exercises and produces mechanical memory. For example, when you see the business scenario of stone throwing, you already know that it is converted into equation solving.

They are extended and generalized in various directions, such as infinite dimensional Lie algebras, Huck algebras, quantum groups or vertex operator algebras. Their structures and representations are usually related to each other in a deep way through D-modules or category equivalence. They are widely used in algebraic geometry, mathematical physics, harmonic analysis, number theory and other fields. The structural results of Lie groups are also extended to locally compact groups. Another important direction is to study the discrete subgroups of Lie groups and their effects on geometric objects.

This also means that God does not know whether the answers to many mathematical problems exist. Because the problem of solving indefinite equations is only a small part of mathematical problems, there are far more problems that can not be judged whether there are solutions in reality than those with answers. It is impossible to solve problems that can not even be judged whether the answer exists or not by calculation. This may be the boundary of mathematics.

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