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# Matrix Rank Tutorial

Matrix is an array of numbers arranged in rows and columns of order m x n (m rows and n columns). Every single number present in the matrix is called as the element or the entry. Below is the example of the matrix of order 3x3: [1 2 3] [4 5 6] [7 8 9]

##### Rank of Matrix:

The matrix rank is determined by the number of independent rows or columns present in it. A row or a column is considered independent, if it satisfies the below conditions. 1. A row/column should have atleast one non-zero element for it to be ranked. 2. A row/column should not be identical to another row/column. 3. A row/column should not be proportional (multiples) of another row/column. 4. A row/column should not be should not be a linear combination of another row/column. A row or a column is ranked only if it meets the above conditions. For example, the rank of the below matrix would be 1 as the second row is proportional to the first and the third row does not have a non-zero element. [1 2 3] [2 4 6] [0 0 0]