RedCrab Math Tutorial
 

Row Operations of Matrices

There are three types of elementary matrix row operations, corresponding to the operations that apply to equations to eliminate variables:
  • Adding a multiple of one row to another row

  • Multiplying of a row by a non-zero scalar

  • Interchange of two rows

These operations can be done manually, but also by matrices multiplication with a given matrix and some modified identity matrix. See the three examples below.
 
Adding a multiple of one row to another:
Placing k in the second column of row 3 of the identity matrix; then multiplying the matrices. This has k-times the values of corresponding elements of row 2 added to those of row 3 of the matrix.

The value of the determinant in the result is identical to the value of the source matrix A.

   

 
Multiplying a row by a non-zero scalar:

The value of the determinant in the result is k-times the value of the source matrix A
 
Interchanging two rows:

The value of the determinant in the result is identical to the value of the source matrix A.
 
More information about determinants
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Matrices Definition
Matrices Calculation
Matrices & Simultaneous Equations
Matrices Determinants
Row Operations of Matrices
Matrices and Geometry, Reflection
Matrices and Geometry, Rotation
 

           
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