Show that the homogeneous system in Problem 1 has a nontrivial solution if and only if ad – bc = 0.
Problem 1
Consider the homogeneous system
ax + by = 0
cx + 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 + y2 is a solution.
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