MATH 2211 Quiz: Quiz1mt210Sample2Ans
Document Summary
Please mark the following statement as true or false: Elementary row operations on an augmented matrix never change the solution set of the associated linear system. You are not expected to provide the follow- ing explanation in a quiz. There are three elementary row operations: replacement, interchange, and scaling. Without loss of generality, let us say we have a system of two equations in two variables: a1x1 + a2x2 = c1 b1x1 + b2x2 = c2. Clearly, if we interchange the equations, a1x1 + a2x2 = c1 b1x1 + b2x2 = c2 b1x1 + b2x2 = c2 a1x1 + a2x2 = c1. I the solution set s1 of the rst system is the same as the solution set s2 of the second system. Let (s1, s2) s1 and (r1, r2) s2. Let us apply scaling where k = 0: a1x1 + a2x2 = c1 b1x1 + b2x2 = c2 k(b1x1 + b2x2) = kc2 a1x1 + a2x2 = c1.
