Our midterm will be 50 minutes, hold in discussion session on Monday. The test range is Givental [LA] Ch 1 and Ch 2, and Ch 3 with the concept of basis, linear independence and span. We will have 5 problems, each worth 20 points.

Problem 1 True or False, please explain your reasoning.

• Let conic curve $C$ be given by the equation $a x^2 + b xy + cy^2=1$, where $a,b,c$ are real numbers. If $a,b,c$ are all positive, then $C$ must be an ellipse.