Explanation Given information: The system of equations is { x + 2 y + z = 15 3 x − y − 3 z = − 8 − 2 x + 4 y − z = − 27 . Formula used: Cramer’s rule: The solution of the system of equations { a 11 x + a 12 y + a 13 z = c 1 a 21 x + a 22 y + a 23 z = c 2 a 31 x + a 32 y + a 33 z = c 3 is given by x = D x D , y = D y D , z = D z D , provided that D = | a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 | ≠ 0 , where D x = | c 1 a 12 a 13 c 2 a 22 a 23 c 3 a 32 a 33 | , D y = | a 11 c 1 a 13 a 21 c 2 a 23 a 31 c 3 a 33 | , D z = | a 11 a 12 c 1 a 21 a 22 c 2 a 31 a 32 c 3 | . Calculation: Compare the system of equations { x + 2 y + z = 15 3 x − y − 3 z = − 8 − 2 x + 4 y − z = − 27 with { a 11 x + a 12 y + a 13 z = c 1 a 21 x + a 22 y + a 23 z = c 2 a 31 x + a 32 y + a 33 z = c 3 . It gives a 11 = 1 , a 12 = 2 , a 13 = 1 , a 21 = 3 , a 22 = − 1 , a 23 = − 3 , a 31 = − 2 , a 32 = 4 , a 33 = − 1 , and c 1 = 15 , c 2 = − 8 , c 3 = − 27 . D = | 1 2 1 3 − 1 − 3 − 2 4 − 1 | = ( − 1 ) 1 + 1 ⋅ 1 ⋅ | − 1 − 3 4 − 1 | + ( − 1 ) 1 + 2 ⋅ 2 ⋅ | 3 − 3 − 2 − 1 | + ( − 1 ) 1 + 3 ⋅ 1 ⋅ | 3 − 1 − 2 4 | = | − 1 − 3 4 − 1 | − 2 ⋅ | 3 − 3 − 2 − 1 | + | 3 − 1 − 2 4 | = 13 − 2 ( − 9 ) + 10 = 13 + 18 + 10 = 41 . Thus, D = | 1 2 1 3 − 1 − 3 − 2 4 − 1 | = 41 ≠ 0

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Chapter 13, Problem 9CR

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To calculate: The solution of the system of equations {x+2y+z=153x−y−3z=− 8− 2x+4y−z=−27.

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Chapter 13, Problem 8CR

Chapter 13, Problem 10CR

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Chapter 13 Solutions

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The solution of the system of equations { x + 2 y + z = 15 3 x − y − 3 z = − 8 − 2 x + 4 y − z = − 27 .

Solution Summary: The author calculates the solution of the system of equations lx+2y+z=15 3x-y-3z =-8 –

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To calculate: The solution of the system of equations {x+2y+z=153x−y−3z=− 8− 2x+4y−z=−27.

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Chapter 13 Solutions