Matrix Chapter-6

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Echelon Form of a Matrix: Let us try to understand, what an echelon matrix is. Echelon matrices come in two forms: the row echelon form and the reduced row echelon form.

Row Echelon Form: A matrix is a Row Echelon is it satisfies the following conditions:

  1. The first non-zero element in each row, called the leading entry, is 1.
  1. Each leading entry is in a column to the right of the leading entry in the previous row
  2. All zero rows are at the bottom of the matrix

Both of the matrices shown below are examples of matrices in row echelon form.

EC_MAT1

Reduced Echelon Form: A matrix is known as reduced echelon form when it satisfies following conditions.

  1. The matrix satisfies conditions for a row echelon form
  2. The leading entry in each row is the only non-zero entry in its columnEC_MAT2

 

 

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