Examples with 0, 1, and infinitely many solutions to linear systems

Learning Objectives:
1) Apply elementary row operations to reduce matrices to the ideal form
2) Classify the solutions as 0, 1, or infinitely many
3) In the infinitely many case, describe the solution set in a nice way using a parameter
4) Identify the features of a reduced matrix to look for to give each of these three possibilities.

This video is part of a Linear Algebra course taught at the University of Cincinnati.

[leopedregosa]

Very few Ph.D. Math Professors can teach math to the point where ordinary mortals will understand. I believe, Dr. Trefor has the gift to teach math. I wish other math professors will re-think and reflect their own ways of teaching by watching how others teach very well.

[dlambert]

4:42 It is not always true that if you have a row of zeros in the row echelon form, there are an infinite number of solutions for the system. For example if we solve the system
x + 2y = 3
4x + 5y = 6
2x + 4y = 6

using the augmented matrix
[1, 2, 3]
[4, 5, 6]
[2, 4, 6]

we obtain a unique solution, despite there being a row of zeros.
[1, 0, -1]
[0, 1, 2 ]
[0, 0, 0 ]

The statement is true though for mxn systems where m <= n.

[moonchildxmochixhobi]

What book would you recommend for practicing. You're an amazing prof by the way. Not to be dramatic, but you're saving my life. lol

[arsal]

hey your channel is like the best i have found after a lot of research, do you have any google drive or dropbox link where you share all the class notes?

[eda]

Thank you sir your explanation is very good