To determine To explain: The reason by which the system could not be solved by matrix inverse methods and solve the system by alternative methods. Explanation Procedure used: First convert the system into a matrix equation of the form A X = B , and then use X = A − 1 B to obtain X . Calculation: It is given that the system of equation are, x 1 − 2 x 2 + 3 x 3 = 1 2 x 1 − 3 x 2 − 2 x 3 = 3 x 1 − x 2 − 5 x 3 = 2 The corresponding coefficient matrix is A = [ 1 − 2 3 2 − 3 − 2 1 − 1 − 5 ] . Note that the formula to solve the system is X = A − 1 B . It is observed that, inverse of the matrix A exists only if the determinant is nonzero. Compute the determinant of the matrix A as, det ( A ) = 1 ( 15 − 2 ) − ( − 2 ) ( − 10 + 2 ) + 3 ( − 2 + 3 ) = 13 + 2 ( − 8 ) + 3 = 0 Thus, as the determinant of the matrix A is 0 the inverse of the matrix A does not exist. Hence, the system could not be solved by matrix inverse methods and use the gauss Jordan method to solve the above system. Form the augmented matrix [ A I ] in order to obtain the inverse of the matrix. [ 1 − 2 3 1 2 − 3 − 2 3 1 − 1 − 5 2 ] Perform row operations on the augmented matrix as, [ 1 − 2 3 1 2 − 3 − 2 3 1 − 1 − 5 2 ] ∼ [ 1 −<

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ISBN: 9781323174869

Author: Barnett

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 4.6, Problem 49E

To determine

To explain: The reason by which the system could not be solved by matrix inverse methods and solve the system by alternative methods.

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Chapter 4.6, Problem 48E

Chapter 4.6, Problem 50E

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Chapter 4 Solutions

COLLEGE MATH FOR MATH2040 RMU PKG

Ch. 4.1 - Solve by graphing and check: 2x − y = −3 x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing: x...Ch. 4.1 - Prob. 3MP Ch. 4.1 - Prob. 4MP Ch. 4.1 - Prob. 5MP Ch. 4.1 - Prob. 6MP Ch. 4.1 - Prob. 7MP Ch. 4.1 - Prob. 1ED Ch. 4.1 - Prob. 2ED Ch. 4.1 - In Problems 1–6, find the x and y coordinates of...

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