suppose 1 2 3

4 5 6

7 8 9

is a matrix. Then what is its rank?

Dear Sumit,

Column rank is defined as maximum number of linearly independent columns.

Row rank is defined as maximum number of linearly independent rows.

In general both of them are equal, hence rank of a matrix = max no. of independent rows or columns.

In the given matrix, any row cannot be obtained by the linear combination of remaining two rows, which means all the three rows are linearly independent, hence there are 3 independent rows which means Rank of the given matrix is 3

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Rohith Gandhi P

rank of the above matrix is 3