Explanation Given Information: The system of linear equations, { x + y − z = − 2 2 x − y + z = 5 − x + 2 y + 2 z = 1 Formula used: Gauss elimination method. Calculation: A system of linear equations can be solved with the help of matrices. It is solved with the help of augmented matrix. A matrix, which is divided into two groups divided by a vertical bar with the coefficients of the variable on one side and constants on the other side is called an augmented matrix. Row indicates coefficient and constant from an equation whereas column indicates all the coefficient of a variable. The coefficient of the missing variable is used as 0 . Augmented matrix for the provided system of equation is written as follows: [ 1 1 − 1 − 2 2 − 1 1 5 − 1 2 2 1 ] Use gauss elimination method to solve the system of linear equations. Convert augmented matrix in row echelon form. Perform the operation − 2 R 1 + R 2 to get, [ 1 1 − 1 − 2 − 2 + 2 − 2 − 1 2 + 1 4 + 5 − 1 2 2 1 ] = [ 1 1 − 1 − 2 0 − 3 3 9 − 1 2 2 1 ] Perform the operation 1 3 R 2 , to get, [ 1 1 − 1 − 2 1 3 × 0 1 3 × ( − 3 ) 1 3 × 3 1 3 × 9 − 1 2 2 1 ] = [ 1 1 − 1 − 2 0 − 1 1 3 − 1 2 2 1 ] Perform R 1 + R 3 , to get, [ 1 1 − 1 − 2 0 − 1 1 3 1 − 1 1 + 2 − 1 + 2 − 2 + 1 ] = [ 1 1 − 1 − 2 0 − 1 1 3

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ISBN: 9780134494890

Author: Blitzer

Publisher: PEARSON

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Chapter 8.1, Problem 21PE

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To calculate: The solution of the system of linear equations x+y−z=−2,2x−y+z=5,−x+2y+2z=1

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Chapter 8.1, Problem 20PE

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Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

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The solution of the system of linear equations x + y − z = − 2 , 2 x − y + z = 5 , − x + 2 y + 2 z = 1

Solution Summary: The author explains how a system of linear equations can be solved with the help of matrices and augmented matrix.

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To calculate: The solution of the system of linear equations x+y−z=−2,2x−y+z=5,−x+2y+2z=1

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