MATH 152 Study Guide - Midterm Guide: Quadratic Function, Linear Map, Parallelogram
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[3] let a = (cid:20) x y x (cid:21) and b = (cid:20) s t s (cid:21). Is it true that ab = ba for all choices of x, y t y, s and t? (b) [3] write down a 2 2 matrix with real entries but with complex eigenvalues. (c) [3] for which values of a does (cid:20) 1 a. For which values of a and b are the vectors . Let t be the triangle in three dimensional space with vertices located at p = . [7] what is the cosine of the angle at the vertex p? (b) [7] what is the area of the triangle. (hint: it is half the area of the parallelogram spanned by two of its sides. ) Consider the quadratic function f (x, y) = 2x2 + y2 + 2xy 8x 6y + 16. Find the minimum value of f and where it occurs.
