Definition of rank of a matrix

Another definition of rank of a matrix

☆Finding rank of matrix

1. Example on minor method

In linear algebra, theis the dimension of its row space or column space. It is important to note that the row space and column space of a matrix have equal dimensions.A nimber r is said to be a rank of a non-zero matrix A ifThere exist at least one minor of order r of A which does not vanish andEvery minor of higher order than r is zero.The rank of a matrix A is denoted by We have The rank of a non-zero matrix is largest order of any non-vanishing minor of the matrix.From the above definition of rank of a matrix, we observe thatThe rank of zero matrix is zero i.e., where O is a zero matrix,The rank of a non-singular matrix of order n is n, , if every minor of order r+1 vanishes, , if there is a minor of order r which does not vanish.Minor methodNormal formEchelon form of matrixDetermine the rank of matrix