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LYDIA BOUROUIBA: Welcome to this presentation on the trace-determinant diagram. So here, youre asked to label the regions and lines of the trace-determinant diagram for a 2 x 2 general system, written in the form x prime equals A*x, and to indicate the stability on your diagram. So here, as a reminder, this system is simply a system of two differential equations in vector form. The derivative of [x, y] equals [a, b; c, d], a 2 x 2 matrix, multiplying the vector [x, y]. Or in another form, it would be x-dot equals f of x, y, and y-dot equals j of x, y, where the t wouldnt appear in f and j here, functions, which means that the system would be autonomous. And were dealing with linear systems. So why dont you pause the video. Take a few minutes remind yourself what the trace-determinant diagram is and how to label it, and Ill be right back. Welcome back. So lets remind ourselves where this trace-determinant diagram comes from. So initially, what we saw before was to solve this syst
