The column vector group of (a, b) is the same as that of (b, a). So their column ranks are equal, and so are the ranks of matrices.

Elementary transformation does not change the rank of matrix, and (b, a) can be obtained by exchanging (a, b) columns, so their ranks are equal.

The column rank of matrix A is the maximum number of linearly independent columns of A. Similarly, the row rank is the maximum number of linearly independent rows of A. Generally speaking, if the matrix is regarded as a row vector or a column vector, the rank is the rank of these row vectors or column vectors, that is, the number of vectors contained in the largest uncorrelated group.

Extended data:

In linear algebra, the row vector is a matrix of 1×n, that is, the matrix consists of a row of n elements, that is, the row vector. The transposition of a row vector is a column vector, and vice versa. The set of all row vectors forms a vector space, which is the dual space of all column vector sets.

Rank rab

When r (a) < When =n-2, the order of the highest order non-zero subformula is < =n-2, any n- 1 subformula is zero, and every element in the adjoint matrix is n- 1 subformula plus a symbol, so the adjoint matrix is a 0 matrix.

When r (a) < When =n- 1, the order of the highest order non-zero sub-formula is < =n- 1, so the sub-formula of order n- 1 may not be zero, so the adjoint matrix may be non-zero (the adjoint matrix must be non-zero when the equal sign holds).

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