Explanation Given Information: The system of equation is, x + y + 4 w = 1 2 x − 2 y − 3 z + 3 w = − 1 4 y + 6 z + w = 4 2 x + 4 y + 9 z = 6 Formula Used: Elementary row operations Type 1: Replacing the row R i by a R i , where a is a nonzero number. Type 2: Replacing the row R i by a R i ± b R j , where a is a nonzero number. Gauss Jordan reduction method Step 1: First clear the fractions or decimals if any, using operations of type 1. Step 2: Select the first nonzero element of the first row as pivot. Step 3: Use the pivot to clear its column using operations of type 2. Step 4: Select the first nonzero element in the second row a pivot and clear its column. Step 5: Select the first nonzero element in the third row a pivot and clear its column. Step 6: Select the first nonzero element in the fourth row a pivot and clear its column. Step 7: Turn all the selected pivot elements into a 1 using operations of type 1. Calculation: Consider the system of equation, x + y + 4 w = 1 2 x − 2 y − 3 z + 3 w = − 1 4 y + 6 z + w = 4 2 x + 4 y + 9 z = 6 The augmented matrix for the given system of equations is, [ 1 1 0 4 1 2 0 2 − 2 4 4 − 3 6 9 3 1 0 − 1 4 6 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by, the selection of the pivot as the first nonzero element of the first row and clear its column. Perform the operation R 2 → R 2 − 2 R 1 and R 4 → R 4 − 2 R 1 [ 1 1 0 4 1 2 0 2 − 2 4 4 − 3 6 9 3 1 0 − 1 4 6 ] → [ 1 1 0 4 1 0 0 0 − 4 4 2 − 3 6 9 − 6 1 − 8 − 3 4 4 ] Next pivot the first nonzero element of the second row and clear its column. Perform the operation R 1 → 4 R 1 + R 2 and R 3 → R 3 + R 2 , [ 1 1 0 4 1 0 0 0 − 4 4 2 − 3 6 9 − 6 1 − 8 − 3 4 4 ] → [ 4 0 − 3 10 1 0 0 0 − 4 0 2 − 3 3 9 − 6 − 5 − 8 − 3 1 4 ] Next clear the leftover element of that column.. Perform the operation R 4 → 2 R 4 + R 2 [ 4 0 − 3 10 1 0 0 0 − 4 0 2 − 3 3 9 − 6 − 5 − 8 − 3 1 4 ] → [ 4 0 − 3 10 1 0 0 0 − 4 0 0 − 3 3 15 − 6 − 5 − 22 − 3 1 5 ] Next pivot the first nonzero element of the third row and clear its column. Perform the operation R 1 → R 1 + R 3 and R 2 → R 2 + R 3 , [ 4 0 − 3 10 1 0 0 0 − 4 0 0 − 3 3 15 − 6 − 5 − 22 − 3 1 5 ] → [ 4 0 0 5 2 0 0 0 − 4 0 0 0 3 15 − 11 − 5 − 22 − 2 1 5 ] Next clear the leftover element of that column. Perform the operation R 4 → R 4 − 5 R 3 [ 4 0 0 5 2 0 0 0 − 4 0 0 0 3 15 − 11 − 5 − 22 − 2 1 5 ] → [ 4 0 0 5 2 0 0 0 − 4 0 0 0 3 0 − 11 − 5 3 − 2 1 0 ] Next simplify the fourth row

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 3.2, Problem 34E

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To calculate: The solution of the given system of equations x+y+4w=1,2x−2y−3z+3w=−1,4y+6z+w=4,2x+4y+9z=6 by the use of Gauss Jordan row reduction.

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Chapter 3.2, Problem 33E

Chapter 3.2, Problem 35E

Chapter 3 Solutions

Finite Mathematics

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The solution of the given system of equations x + y + 4 w = 1 , 2 x − 2 y − 3 z + 3 w = − 1 , 4 y + 6 z + w = 4 , 2 x + 4 y + 9 z = 6 by the use of Gauss Jordan row reduction.

Solution Summary: The author calculates the solution of the given system of equations by the use of Gauss Jordan row reduction.

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To calculate: The solution of the given system of equations x+y+4w=1,2x−2y−3z+3w=−1,4y+6z+w=4,2x+4y+9z=6 by the use of Gauss Jordan row reduction.

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Chapter 3 Solutions