Elementary Operations (Row/Column Operations) on Matrices

Row operations:

a)      Interchanging of two rows: We can interchange any two rows in a matrix. The interchanging of i^th and j^th rows is symbolically denoted by R_i ↔ R_j.

b)      Multiplying a row by a scalar: We can multiply any row of a scalar. Multiplying i^th row by a scalar ‘m’ is symbolically denoted by R_i→mR_i.

c)      Multiplying a row by a scalar and adding the elements of this row to the corresponding elements of the other row:  Multiplying j^th row by a scalar ‘m’ and adding it to the i^th row is symbolically denoted by R_i→R_i+mR_j

Column operations:

a)      Interchanging of two columns: We can interchange any two columns in a matrix. The interchanging of i^th and j^th columns is symbolically denoted by C_i ↔ C_j.

b)      Multiplying a column by a scalar: We can multiply any column of a scalar. Multiplying i^th column by a scalar ‘m’ is symbolically denoted by C_i→mC_i.

c)      Multiplying a column by a scalar and adding the elements of this column to the corresponding elements of the other column:  Multiplying j^th column by a scalar ‘m’ and adding it to the i^th column is symbolically denoted by C_i→C_i+mC_j.