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Example of ERO

Row Equivalent Matrices

Matrix A

Elementary Row Operation

Inverse matrix A

Row equivalent matrices is the condition where 2 matrices can be transform from one to another by using ERO

Conclusion

ERO is used in Gaussian Elimination to reduce matrix to row echelon form.

There are 3 types of ERO:

  • Switching a row to another row
  • Multiple each row with non-zero constant
  • Multiple all intries pf a rpw and add the product to another row

We can conclude that invertible and non-invertible matrices can be find by reducing the matrix to row echelon form or finding its determinant.

This 2 method can be find by using Elementary Row Operation.

Row equivalent form is a pair of matrices that can transform one to another.

Matrix

Row Echelon Form

Matrix is defined as a rectangular array of elements in 2 dimensional arrays of numbers arranged in column and row.

Matrix can be reduced to row echelon form by ERO.

Example of Row Echelon Form :

Invertible and Non-Invertible Matrix

There are 2 method to determine whether the matrices are invertible or non-invertible:

  • Reduce the matrices to row echelon form
  • Finding its determinant

These 2 method can be find by using ERO (Elementary Row Operation

Determinant

We can determine whether the matrices invertible or non-invertible

Invertible

Determinant can be evaluated as the sum of the products of the elements of any one row with their respective.

It can also deduce whether the matrices have inverse or vice versa. If it have determinant, it is invertible and vice versa.

Non-Invertible

Invertible and Row Equivalent Matrix

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