What is the rank of a matrix and how it can be found?What is its uses?Please clarify with examples.
The rank of a matrix is the number of linearly independent rows (or columns) of that matrix. This is usually found by the Gauss elimination method, but other methods exist for more complicated/exotic circumstances.
Matrix rank can be used to characterize some properties of a matrix, or determine the number of solutions to a system of linear equations represented by the matrix (which is the typical application on first encounters with matrices).