Matrix echolon form

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

Here the instructor says “important thing is that the pivots are now one and they’re in the same location because dividing by a number one turn a zero into a non-zero or a non-zero into a zero.”

  1. does pivot mean non-zero numbers in the main diagnal?
  2. We divided the three rows by 3,1,(-4) respectively, why it says we divided them by 1?
  3. Why dividing by a number one turn a zero into a non-zero or a non-zero into a zero?

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2

This is one of those errors in the lectures that I mentioned.

3

So it means:
question 2 should be corrected to divide each row by first non-zero number?
question 3 should be ignored?
how about question 1?

4

Yes, you’re right about questions 2 and 3. For q1, the pivot is on the main diagonal, but if the matrix is singular, it may not always be non-zero. Or you may have to rearrange the rows in order to proceed by looking down the pivot column from the current row and switch with the first row you find that has a non-zero value in the pivot column. This will be covered in the assignment if it’s not mentioned in the lectures.

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