Solution Found!
Show that the homogeneous system in has a nontrivial
Chapter 3, Problem 37P(choose chapter or problem)
Show that the homogeneous system in has a nontrivial solution if and only if ad – bc = 0. Consider the homogeneous systemax + by = 0cx + dy = 0.(a) If x = x0 and y = y0 is a solution and k is a real number, then show that x = kx0 and y = ky0 is also a solution.________________(b) If x = x1, y = y1 and x = x2, y = y2 are both solutions, then show that x = x1 + x2, y = y1 + y2is a solution.
Questions & Answers
QUESTION:
Show that the homogeneous system in has a nontrivial solution if and only if ad – bc = 0. Consider the homogeneous systemax + by = 0cx + dy = 0.(a) If x = x0 and y = y0 is a solution and k is a real number, then show that x = kx0 and y = ky0 is also a solution.________________(b) If x = x1, y = y1 and x = x2, y = y2 are both solutions, then show that x = x1 + x2, y = y1 + y2is a solution.
ANSWER:SOLUTIONStep 1 of 2In this problem, we have to show that the given homogeneous system has a non-trivial solution if and only if ________________