Explanation Given: The Linear equation system is, a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 Proof: The solution of given system use Cramer舗s rule, | a 1 b 1 a 2 b 2 | = | c 1 c 2 | x = D x D and y = D y D D = | a 1 b 1 a 2 b 2 | = a 1 ⋅ b 2 − b 1 ⋅ a 2 D x = | c 1 b 1 c 2 b 2 | = c 1 ⋅ b 2 − b 1 ⋅ c 2 D y = | a 1 c 1 a 2 c 2 | = a 1 ⋅ c 2 − c 1 ⋅ a 2 So, x = c 1 ⋅ b 2 − b 1 ⋅ c 2 a 1 ⋅ b 2 − b 1 ⋅ a 2 (i) y = a 1 ⋅ c 2 − c 1 ⋅ a 2 a 1 ⋅ b 2 − b 1 ⋅ a 2 (ii) Now consider the first equation as a sum of two equation i.e. a 1 x + b 1 y = c 1 As a sum of two equation, a 3 x + b 3 y = c 3 a 4 x + b 4 y = c 4 Where, a 1 = a 3 + a 4 ( i i i ) b 1 = b 3 + b 4 ( i v ) c 1 = c 3 + c 4 ( v ) So, equation 1 can be written as, ( a 3 + a 4 ) x + ( b 3 + b 4 ) y = c 3 +

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Chapter 9.5, Problem 86E

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To Prove: Use Cramer舗s Rule to prove that if the first equation of the system is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

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Chapter 9.5, Problem 85E

Chapter 9.5, Problem 87E

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Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Prob. 3CVC Ch. 9.1 - Prob. 4CVC Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 18, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...

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To Prove: Use Cramer舗s Rule to prove that if the first equation of the system is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

Solution Summary: The author explains how Cramer's Rule proves that if the first equation is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

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To Prove: Use Cramer舗s Rule to prove that if the first equation of the system is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

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Chapter 9 Solutions