Explanation Given Information: The system of equation is, − 1 2 x + y − 1 2 z = 0 − 1 2 x − 1 2 y + z = 0 x − 1 2 y − 1 2 z = 0 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 by using type 1 operation. Step 2: Select the first nonzero element of the first row as pivot element. Step 3: Use the pivot to clear its column using type 2 operation. Step 4: Select the first nonzero element in the second row a pivot and clear its column. Step 5: Turn all the selected pivot elements into a 1 using operations of type 1. Calculation: Consider the system of equation, − 1 2 x + y − 1 2 z = 0 − 1 2 x − 1 2 y + z = 0 x − 1 2 y − 1 2 z = 0 The augmented matrix for the system of equations is, [ − 1 2 1 − 1 2 0 − 1 2 1 − 1 2 − 1 2 1 − 1 2 0 0 ] Apply Gauss Jordan reduction method to get the solution of the system of equation. Begin by the simplification of the first row and second row. Perform the operations R 1 → 2 R 1 and R 2 → 2 R 2 , [ − 1 2 1 − 1 2 0 − 1 2 1 − 1 2 − 1 2 1 − 1 2 0 0 ] → [ − 1 2 − 1 0 − 1 1 − 1 − 1 2 2 − 1 2 0 0 ] Next simplify the third row. Perform the operation R 3 → 2 R 3 , [ − 1 2 − 1 0 − 1 1 − 1 − 1 2 2 − 1 2 0 0 ] → [ − 1 2 − 1 0 − 1 2 − 1 − 1 2 − 1 0 0 ] Next pivot the first nonzero element of the first row and clear its column

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 3.2, Problem 19E

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To calculate: The solution of the system of equations −12x+y−12z=0,−12x−12y+z=0,x−12y−12z=0 by the use of Gauss Jordan row reduction.

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Chapter 3.2, Problem 18E

Chapter 3.2, Problem 20E

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The solution of the system of equations − 1 2 x + y − 1 2 z = 0 , − 1 2 x − 1 2 y + z = 0 , x − 1 2 y − 1 2 z = 0 by the use of Gauss Jordan row reduction.

Solution Summary: The author explains the Gauss Jordan method of calculating the solution of the system of equations.

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To calculate: The solution of the system of equations −12x+y−12z=0,−12x−12y+z=0,x−12y−12z=0 by the use of Gauss Jordan row reduction.

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Chapter 3 Solutions