Use iii of Theorem 831 to find the rank of the given matrix

Use (iii) of Theorem 8.3.1 to find the rank of the given matrix. (3 1 - 1 4)

Solution

Given matrix =     3   -1

                          1    4

   det = 3.4 - 1.-1 = 12 +1 =13

Hence, matrix is non-singular.

A square matrix A_n×n is non-singula then its rank is equal to n.

Therefore,

  rank of the matrix = 2

             (or)

Rank of matrix = no of independent rows (or) columns.

If one row is a multiple of another, then they are not independent. Equivalently, If one column is a multiple of another, then they are not independent.

In the above matrix , no of independent rows (or) columns = 2

Therefore,

rank of the matrix = 2