![]() ![]() 9.Įxplain why the scalar used in a Type (I) row operation must be nonzero. Use part (a) and induction to prove part (2) of Theorem 2.1. (Hint: Use the fact from Section 1.5 that the kth row of ( AB) = ( kth row of A) B.) (b) Prove part (1) of Theorem 2.1 by showing that R( AB) = ( R( A)) B for each type of row operation ((I), (II), (III)) in turn. This exercise asks for proofs for parts of Theorem 2.1. Compute R( AB) and ( R( A)) B to verify that they are equal, if Find the equation of the circle that goes through the points (6,8),(8,4), and (3,9). The general equation of a circle is x 2 + y 2 + ax + by = c. Find the correct number of each type of coin. There are twice as many dimes as quarters, and the total number of nickels and quarters is twenty more than the number of dimes. Solve the following problem by using a linear system: A certain number of nickels, dimes, and quarters totals $17. Suppose that each of the following is the final augmented matrix obtained after Gaussian Elimination. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. In each case, indicate whether the system is consistent or inconsistent. ![]() Use Gaussian Elimination to solve each of the following systems of linear equations. ![]()
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