Linear algebra (1)--the same solution deformation of a set of equations

The first self-taught Tongji 5 version of the linear algebra, from the beginning to look, also a little puzzled, suddenly there are many determinant appear, in fact, the definition of the real does not understand.

Refer to the Li Shangzhi teacher's linear Algebra 2 video and make some notes to enhance understanding.

1. The number table in the determinant, now appears to be the coefficients of the multivariate one-time equations, is simply written for easy writing.

2. Solving the determinant is also the solution of the equation group

The same solution deformation of the equations, by the same solution deformation of the equations, using the Gaussian elimination method, the gradual transformation, each step is reversible, the final transformation of all the solutions of the equation Group

If the equation group (i) has a common solution, then this public solution is the solution of any linear combinatorial equations of the equation group (i);

If the equations (i) are linearly combined with the equations (ii), then the equations (i) are equivalent to the equations (ii), (which is one thing that can be extrapolated backwards)

Here to illustrate what is a "linear combination"

Linear combinations include

1. Addition of equations

2. Multiply the equation by the constant: multiply the two sides by Lamda, and the equation is equivalent to the previous equation.

Now we get the general method to deal with the multivariate one-time equation by Gaussian elimination method: kick, three strokes!

The first move: in the equations, the positions of any two equations are exchanged, and the equations are not changed;

The second trick: in the equation set, multiply one of the equations by a non-0 constant, not 0 constant, not 0 constant! , the whole equation group is unchanged;

The third trick: in the equations, multiply one of the equations by LAMDA, plus another equation in the equation set, the equations are the same. The third trick is most used in solving the equation process.

In the process of the same solution transformation of the equations, the writing format is fastidious

1, when writing, relative to the same meta-position,

2, in the process of elimination, the number of yuan is constantly reduced, to the end, only the last one, is a group of equations of one of the solutions, and then this in turn back to the upper

Equations in the equation set, the final result can be obtained.

3, the equation group can also be another method, continue to eliminate the other elements, and finally get the solution!

4,ps: Maintains a record of the operation of the equation in the process of eliminating the element.

Linear algebra (1)--the same solution deformation of a set of equations