Let A be a symmetric 2 2 matrix and let k be a scalar. Prove that the graph of the
Chapter 5, Problem 5.5.87(choose chapter or problem)
Let A be a symmetric 2 2 matrix and let k be a scalar. Prove that the graph of the quadratic equation xT Ax k is (a) a hyperbola if k 0 and det A 0 (b) an ellipse, circle, or imaginary conic if k 0 and det A 0 (c) a pair of straight lines or an imaginary conic if k 0 and det A 0 (d) a pair of straight lines or a single point if k 0 and det A 0 (e) a straight line if k 0 and det A 0 [Hint: Use the Principal Axes Theorem.]
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