Question

prove that rank of a matrix A is equal
to maximum number of linearly
independent column vector of A​

Answer 1

Answer:

The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in its row echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows. Consider matrix A and its row echelon matrix, Aref.