
The rank of the matrix A is the largest of the orders of its minors that are not equal to zero.
Denotes the rank of the matrix: r (A) or rang (A).
Methods for finding the rank of the matrix
Elementary transformation method for finding the rank of a matrix
The method of elementary transformations for finding the rank of a matrix is that matrix A is led to a stepwise form using elementary transformations; the number of nonzero rows of the obtained step matrix is the desired rank of the matrix A.
The method of bordering minors for finding the rank of the matrix A is as follows. It is necessary:
As elementary algebra help service says: find some firstorder minor M1 (i.e. matrix element) that is nonzero. If there is no such minor, then the matrix A is zero and r (A) = 0.
Calculate 2nd order minors containing M1 (bordering M1) until there is a nonzero minor M2. If there is no such minor, then r (A) = 1, if there is, then r (A) ≥ 2. and so on.
Calculate (if they exist) the minors of the ko order, surrounding the minor of Mk1> 0. If there are no such minors, or they are all equal to zero, then r (A) = k1; if at least one such minor Mk> 0, then r (A) = k, and the process continues.

Elementary algebra
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