Consider the system of linear equations a11x1 + a12x2 = b1, a21x1 + a22x2 = b2. Define
Chapter 2, Problem 29(choose chapter or problem)
Consider the system of linear equations a11x1 + a12x2 = b1, a21x1 + a22x2 = b2. Define ,1, and 2 by = a11a22 a12a21, 1 = a22b1 a12b2, 2 = a11b2 a12b1. (a) Show that the given system has a unique solution if and only if = 0, and that the unique solution in this case is x1 = 1/, x2 = 2/. (b) If = 0 and a11 = 0, determine the conditions on 2 that would guarantee that the system has(i) no solution, (ii) an infinite number of solutions. (c) Interpret your results in terms of intersections of straight lines.
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