# Negative Determinant on XY Graph

Can someone help me understand the negative Determinant in this slide when it comes to how it is depicted on the XY graph. I understand that the numeric Determinant is negative, but what does it mean in terms of graph intuition?

Anyone? Mr. Serrano, your explanations do not much make sense at times…how is the negative area shown in the graph? Seriously, Khan Academy is way better when it comes to truly understanding the subject matter. I think it is rather flippant how casually it is mentioned here as supplemental material, when it is free and vastly superior to Serrano’s stuff…just a little sad that you have to pay for something inferior that references something free and better.

The graphical representation of a determinant of a 2x2 matrix is

the area of the image of the fundamental basis formed by the unit square on the left.

And a negative determinant will have no graphical difference with a positive determinant. The image below can have a determinant of either 5 or -5.

That’s why we need the transformation matrix for the order (clockwise or counterclockwise) of the vectors to distinguish a positive and a negative determinant. I hope it helps!

Well, for what it is worth, the explanations by the Coursera staff have not helped me, so I am going to leave this out there:

Distinguishing a positive or negative area by flipping the parallelogram is one thing, but what does a negative area on a graph mean?