Confusion about Row echelon form

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
1

Does Row echelon form matrix have only 1s and 0s in the main diagonal? Or does it also have other numbers in the main diagonal?

Also how do i stop the 0 s in the leftmost lower triangle from getting converted to a different number while I am trying to convert the other numbers of the triangle to 0?

2

Row echelon form has the following characteristics, from the lectures:

  • Zero rows at the bottom
  • Each row has a pivot, which is the leftmost non-zero entry
  • Every pivot to is to the right of the pivot in the row above it.
  • The rank is the number of pivot.
  • in general, pivots greater than one are allowed. This last point answers your question on whether the diagonals can contain numbers other than 0 and 1.

Reduced row echelon form has all pivots equal to 1 and all numbers above a pivot equal to 0.

While trying to change a matrix to its row echelon form, just make sure that you follow the operations that preserve singularity and you are good.

3

Continuing on this thread. In the lecture W2 Row ecehlon form for general case. Why is only the top-left to bottom-right diagonal considered to get the rank of a matrix.
Say For example 1 below a row echelon form of a matrix is given

[1 1 1
 0 0 0
 0 0 0]

why is the rank calculated to be 1? why isn’t the 1 at the top-right location and the diagonal from top-right to bottom-left considered?
The reason I ask is for the below example(2)

[1 1 1
 0 0 1
 0 0 0]

the rank is caluclated as 2. How?

im just trying to understand

  1. why is only the top-left to bottom-right diagonal considered for calculating the rank of a matrix.
  2. There are M+N - 1 diagonal in a square matrix(represented as: M*N), why aren’t all (from top left to bottom right) considered?
    hope this helps.
4

nevermind, i think to answer my own question,
To calculate the rank of a matrix:

  1. calculate the REF
  2. calculate number of NON-ZERO rows
5

It’s good you solved your own question.

Tip: In the future, avoid replying on a thread that has gone cold. This one hasn’t been updated in two years.

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