Explanation Approach: Cramer’s Rule: Cramer’s Rule is a method of solving system of equations using determinants. Ex: p x + q y = a r x + s y = b Here they have two equations with two variables x and y . It has one single solution given as x = a q b s p q r s , y = p a r b p q r s This can also be written as x = D x D , y = D y D where D x = a q b s , D y = p a r b , D = p q r s As you observe that the denominators are same for x and y . It is nothing but the determinant of the coefficient matrix. Calculation: Given x 2 + y 5 + z 3 = 17 x 5 + y 2 + z 5 = 32 x + y 3 + z 2 = 30 x = D x D , y = D y D , z = D z D D x is the determinant formed by replacing the coefficients of x with the constants. In the similar manner, D y is the determinant formed by replacing the coefficients of y with the constants and D z is the determinant formed by replacing the coefficients of z with constants. D is the determinant of the coefficient matrix. D x = 17 1 5 1 3 32 1 2 1 5 30 1 3 1 2 , D y = 1 2 17 1 3 1 5 32 1 5 1 30 1 2 , D Z = 1 2 1 5 17 1 5 1 2 32 1 1 3 30 , D = 1 2 1 5 1 3 1 5 1 2 1 5 1 1 3 1 2 Let’s calculate the determinant by expanding by cofactors. x = 17 1 5 1 3 32 1 2 1 5 30 1 3 1 2 1 2 1 5 1 3 1 5 1 2 1 5 1 1 3 1 2 Calculate the determinant in the numerator and denominator by expanding along its first row. Check i + j for the signs of cofactors. x = 17 1 2 1 5 1 3 1 2 + 1 5 - 32 1 5 30 1 2 + 1 3 32 1 2 30 1 3 1 2 1 2 1 5 1 3 1 2 + 1 5 - 1 5 1 5 1 1 2 + 1 3 1 5 1 2 1 1 3 x = 17 1 2 × 1 2 - 1 5 × 1 3 + 1 5 - 32 × 1 2 - 1 5 × 30 + 1 3 32 × 1 3 - 1 2 × 30 1 2 1 2 × 1 2 - 1 5 × 1 3 + 1 5 - 1 5 × 1 2 - 1 5 × 1 + 1 3 1 3 × 1 5 - 1 × 1 2 x = 17 1 4 - 1 15 + 1 5 - 16 - 6 + 1 3 ( 32 3 - 15 ) 1 2 1 4 - 1 15 + 1 5 - 1 10 - 1 5 + 1 3 1 15 - 1 2 x = 17 11 60 + 1 5 - 10 + 1 3 - 13 3 1 2 11 60 + 1 5 - - 1 10 + 1 3 - 13 30 x = 187 60 - 2 - 13 9 11 120 + 1 50 - 13 90 x = 561 - 360 - 260 180 165 + 36 - 260 1800 x = - 59 180 - 59 1800 x = - 59 180 × - 1800 59 x = 10 y = 1 2 17 1 3 1 5 32 1 5 1 30 1 2 1 2 1 5 1 3 1 5 1 2 1 5 1 1 3 1 2 Calculate the determinant in the numerator and denominator by expanding along its first row. Check i + j for the signs of cofactors

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 6.5, Problem 48E

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The solution of the system x2+y5+z3=17x5+y2+z5=32x+y3+z2=30 using Cramer’s Rule.

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Chapter 6.5, Problem 47E

Chapter 6.5, Problem 49E

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The solution of the system x 2 + y 5 + z 3 = 17 x 5 + y 2 + z 5 = 32 x + y 3 + z 2 = 30 using Cramer’s Rule.

Solution Summary: The author explains Cramer's Rule as a method of solving system of equations using determinants.

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To find:

The solution of the system x2+y5+z3=17x5+y2+z5=32x+y3+z2=30 using Cramer’s Rule.

Want to see the full answer?

Chapter 6 Solutions

The solution of the system x 2 + y 5 + z 3 = 17 x 5 + y 2 + z 5 = 32 x + y 3 + z 2 = 30 using Cramer’s Rule.

Solution Summary: The author explains Cramer's Rule as a method of solving system of equations using determinants.

Videos

To find: The solution of the system x2+y5+z3=17x5+y2+z5=32x+y3+z2=30 using Cramer’s Rule.

Want to see the full answer?

Chapter 6 Solutions

To find:

The solution of the system x2+y5+z3=17x5+y2+z5=32x+y3+z2=30 using Cramer’s Rule.