Problem 12. (8 points) The reduced row-echelon forms of the augmented matrices o

Question

Problem 12. (8 points) The reduced row-echelon forms of the augmented matrices of four systems are given below. How many solutions does each system have? 1 0 12 0 ] 0 1 0 0 00 01 a. O A. Infinitely many solutions B. Unique solution O C. No solutions D. None of the above

Explanation / Answer

Dear Student Thank you for using Chegg !! a) Let the 4 parameters of the reduced row echlon form be w , x ,y ,z Now since the leading coefficient of x and y is 0 we assume w =s and x = t All the solutions shall be in terms of s and t Hence there shall be infinitely many solutions for the given equation set represented by row echlon matrix option A is correct b) Since number of rows of the matrix does not equalize with the number of parameters governed by the number of columns There shall be NO Solution for the given set of equations c) Refer to explanation in part a also. Let the parameters defined by 3 rows be x, y , z Since there is no leading coefficient for thrid row in reduced row echlon matrix => z = t All solutions of x and y shall be in terms of t Hence these system of equations have infinite solutions d) Since there are only 2 rows and the leading coefficient of both the rows are well defined There shall be nique solution to the set of equations if paraeters are assumed to be x and y then x = 11 y = -16

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