If there are infinitely many solutions, you can tell by converting the matrix back into a system of equations and solving the system. If you come up with a true statement such as 2=2, then you know that the matrix has infinitely many solutions.
Alternately, if you can use this method:
An example of the matrix with infinitely many solutions is this:
A system has no solution if the numbers are all zeros except for the last column that represents the constant.
This is an example of a system with no solution:
You can see that in the final form, the third row is all zeros except for the fourth column,
Math joke of the day:
Wow your pictures really helped me out. That joke is also hilarious, thank you!
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