Explanation Given Information: The system of equation is x − 1 2 y + z = 0 1 2 x − 1 2 z = − 1 3 2 x − 1 2 y + 1 2 z = − 1 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. Calculation: Consider the system of equations, x − 1 2 y + z = 0 1 2 x − 1 2 z = − 1 3 2 x − 1 2 y + 1 2 z = − 1 The augmented matrix for the given system of equations is [ 1 − 1 2 1 0 1 2 0 − 1 2 − 1 3 2 − 1 2 1 2 − 1 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by the simplification of the first and second row by the operation R 1 → 2 R 1 , R 2 → 2 R 2 , [ 1 − 1 2 1 0 1 2 0 − 1 2 − 1 3 2 − 1 2 1 2 − 1 ] → [ 2 − 1 2 0 1 0 − 1 − 2 3 2 − 1 2 1 2 − 1 ] Simplify the third row by the operation R 3 → 2 R 3 , [ 2 − 1 2 0 1 0 − 1 − 2 3 2 − 1 2 1 2 − 1 ] → [ 2 − 1 2 0 1 0 − 1 − 2 3 − 1 1 − 2 ] Select the first nonzero element of first row and clear its column

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Chapter 3, Problem 15RE

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To calculate: The solution of the system of linear equations consisting of x−12y+z=0,12x−12z=−1 and 32x−12y+12z=−1.

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Chapter 3, Problem 14RE

Chapter 3, Problem 16RE

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The solution of the system of linear equations consisting of x − 1 2 y + z = 0 , 1 2 x − 1 2 z = − 1 and 3 2 x − 1 2 y + 1 2 z = − 1 .

Solution Summary: The author explains how to calculate the solution of the system of linear equations consisting of x-12y+z=0.

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To calculate: The solution of the system of linear equations consisting of x−12y+z=0,12x−12z=−1 and 32x−12y+12z=−1.

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Chapter 3 Solutions