How to judge the linear independence of vector groups

Firstly, the column vectors of a vector group are put together to form a matrix, and the elementary row transformation is carried out to become a row ladder matrix. If the rank of matrix A is less than the number m of vectors, then the vector groups are linearly related. For any vector group, it is either linearly independent or linearly related. When the vector group contains only one vector A and A is zero, it is called linear correlation of A; If a≠0, it is said that A is linearly independent.

Any vector group containing zero vectors is linearly related. Vector groups containing the same vector must be linearly related. Increasing the number of vectors will not change the correlation of vectors. (Note that the original vector group is linearly related. )

Extended data:

1, vectors A 1, A2, ..., an(N≥2) are linear combinations of one of these n vectors and the other (n- 1) vectors.

2. The sufficient condition of vector linear correlation is that it is a zero vector.

3. The necessary and sufficient condition for the straight lines of two vectors A and B is that A and B are linearly correlated.

4. The necessary and sufficient condition for the * * * surface of three vectors A, B and C is that A, B and C are linearly correlated.

5. The vector of n+1n dimension is always linearly related.