Matrix is equivalent to vector, determinant is equivalent to the module of vector.
Generally, determinant is introduced first, and then matrix is introduced. I don't think this is a good idea. You should know the matrix first.
At first, in practical application, there will be many unknowns. In order to solve these unknowns by formulas, simultaneous equations are used. For example, to know the value of x 1, x2, the simultaneous equation {a * x1+b * x2 = i.
c*x 1+d*x2=j},
Solve it like this. But in real life, especially when encountering some complicated processes, there will be many unknowns, so there will be many equations to be solved at the same time.