Explanation Given: The system of equations is { x − z = 3 2 x + y = − 3 2 y − z = 7 . Procedure used: “Solving a system of linear equations using matrices: Step1: Write the augmented matrix of the system. Step 2: Perform row operations so the entry in row 1, column 1 is 1. Step 3: Perform row operations so all the entries below the 1 in row 1, column 1 are 0s. Step 4: Perform row operations so the entry in row 2, column 2 is 1. Be sure the entries in column 1 remain unchanged. Step 5: If solving a system of three linear equations, continue to perform row operations so that the entry below the 1 in row 2, column 2, is 0. Step 6: Perform row operations so the entry in row 3, column 3 is 1. Step 7: Write the augmented matrix in row echelon form, write the corresponding system of equations. Substitute to find the values of the variables. Step 8: Check the answer”. Calculation: Obtain the solution for the system of equations as follows. First, write the augmented matrix for the given system. To obtain the augmented matrix the given system of equations is represented in the matrix form as A X = B that is, [ 1 0 − 1 2 1 0 0 2 − 1 ] [ x y z ] = [ 3 − 3 7 ] Here, A = [ 1 0 − 1 2 1 0 0 2 − 1 ] , X = [ x y z ] and B = [ 3 − 3 7 ] . Now, the augmented matrix for the given system of equations can be written as, [ 1 0 − 1 3 2 1 0 − 3 0 2 − 1 7 ] . The entry in row 1, column 1 is 1. The entry in row 2, column 1 and row 3, column 1 should be 0, so apply row operation R 2 = − 2 r 1 + r 2 as, R 2 = − 2 r 1 + r 2 [ 1 0 − 1 3 0 1 2 − 9 0 2 − 1 7 ] Now, the entry of row 3, column 2 is made 0 by the following row operations R 3 = − 2 r 2 + r 3 , R 3 = − 2 r 2 + r 3 [ 1 0 − 1 3 0 1 2 − 9 0 0 − 5 25 ] Use the row operation R 3 = − 1 5 r 3 as, R 3 = − 1 5 r 3 [ 1 0 − 1 3 0 1 2 − 9 0 0 1 − 5 ] The system of equations that corresponds to the above matrix is, { x − z = 3 y + 2 z = − 9 z = − 5 Substitute z = − 5 in y + 2 z = − 9

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Ch. C.1 - Prob. 11E Ch. C.1 - Prob. 12E Ch. C.1 - Prob. 13E Ch. C.1 - Prob. 14E Ch. C.1 - Prob. 15E Ch. C.1 - Prob. 16E Ch. C.1 - 17.While a system of equations is solved, a false...Ch. C.1 - Prob. 18E Ch. C.1 - Prob. 19E Ch. C.1 - Prob. 20E Ch. C.1 - Prob. 21E Ch. C.1 - In Problems 2022, solve the system. Draw a graph...Ch. C.1 - Prob. 23E Ch. C.1 - Prob. 24E Ch. C.1 - Prob. 25E Ch. C.1 - Prob. 26E Ch. C.1 - Prob. 27E Ch. C.1 - Prob. 28E Ch. C.1 - Prob. 29E Ch. C.1 - Prob. 30E Ch. C.1 - Prob. 31E Ch. C.1 - Prob. 32E Ch. C.1 - Prob. 33E Ch. C.1 - Prob. 34E Ch. C.1 - Prob. 35E Ch. C.1 - Prob. 36E Ch. C.1 - In Problems 3542, solve the system of equations...Ch. C.1 - Prob. 38E Ch. C.1 - Prob. 39E Ch. C.1 - Prob. 40E Ch. C.1 - Prob. 41E Ch. C.1 - Prob. 42E Ch. C.1 - Prob. 43E Ch. C.1 - Prob. 44E Ch. C.1 - Prob. 45E Ch. C.1 - Prob. 46E Ch. C.1 - Prob. 47E Ch. C.1 - Prob. 48E Ch. C.1 - Prob. 49E Ch. C.1 - Prob. 50E Ch. C.1 - Prob. 51E Ch. C.1 - Prob. 52E Ch. C.1 - Prob. 53E Ch. 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