For the equation ax^2 + bxy + cy^2 = 0, let A = [a b/2 b/2 c] (A is a 2x2 matrix) Show that if det(A) = 0, then the graph of ax^2 + bxy + cy^2 = 0 is a line. Show that if det(A) != 0, then the graph of ax^2 + bxy + cy^2 = 0 is two intersecting lines.

For the equation ax^2 + bxy + cy^2 = 0, let A = [a b/2 b/2 c] (A is a 2x2 matrix) Show that if det(A) = 0, then the graph of ax^2 + bxy + cy^2 = 0 is a line. Show that if det(A) != 0, then the graph of ax^2 + bxy + cy^2 = 0 is two intersecting lines.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For the equation ax^2 + bxy + cy^2 = 0, let A = [a b/2 b/2 c]

(A is a 2x2 matrix)

Show that if det(A) = 0, then the graph of ax^2 + bxy + cy^2 = 0 is a line.

Show that if det(A) != 0, then the graph of ax^2 + bxy + cy^2 = 0 is two intersecting lines.

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