Explanation Given Information: The system of equation is, 0.5 x + 0.1 y = 1.7 0.1 x − 0.1 y = 0.3 x + y = 11 3 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, 0.5 x + 0.1 y = 1.7 0.1 x − 0.1 y = 0.3 x + y = 11 3 The augmented matrix for the system of equations is, [ 0.5 0.1 1.7 0.1 1 − 0.1 1 0.3 11 / 3 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by the simplification of the first row and second row. Perform the operations R 1 → 10 R 1 and R 2 → 10 R 2 , [ 0.5 0.1 1.7 0.1 1 − 0.1 1 0.3 11 / 3 ] → [ 5 1 17 1 1 − 1 1 3 11 / 3 ] Next simplify the third row. Perform the operation R 3 → 3 R 3 , [ 5 1 17 1 1 − 1 1 3 11 / 3 ] → [ 5 1 17 1 3 − 1 3 3 11 ] Next pivot the first nonzero element of the first row and clears its column. Perform the operations R 2 → 5 R 2 − R 1 and R 3 → 5 R 3 − 3 R 1 , [ 5 1 17 1 3 − 1 3 3 11 ] → [ 5 1 17 0 0 − 6 12 − 2 4 ] Next simplify the second and third row

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Chapter 4.2, Problem 13E

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To calculate: The solution of the system of equations 0.5x+0.1y=1.7,0.1x−0.1y=0.3,x+y=113 by the use of Gauss Jordan row reduction.

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Chapter 4.2, Problem 12E

Chapter 4.2, Problem 14E

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The solution of the system of equations 0.5 x + 0.1 y = 1.7 , 0.1 x − 0.1 y = 0.3 , x + y = 11 3 by the use of Gauss Jordan row reduction.

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

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To calculate: The solution of the system of equations 0.5x+0.1y=1.7,0.1x−0.1y=0.3,x+y=113 by the use of Gauss Jordan row reduction.

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Chapter 4 Solutions