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A linear system is described by the following equations: 6x2 + 2x3 = 10 3x1 + 2x2 + x3 = 6 4x1 + 5x2 + 2x3 = 9. Based on these equations, answer the questions below. (a) From the given linear equations, identify the matrices A, x and b such that the linear system can be expressed as a matrix equation. (b) Examine if the matrix A has any pivoting problem? Explain why or why not?

A linear system is described by the following equations: 6x2 + 2x3 = 10 3x1 + 2x2 + x3 = 6 4x1 + 5x2 + 2x3 = 9. Based on these equations, answer the questions below. (a) From the given linear equations, identify the matrices A, x and b such that the linear system can be expressed as a matrix equation. (b) Examine if the matrix A has any pivoting problem? Explain why or why not?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 93E
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Need ans for part a and b
A linear system is described by the following equations: 6x2 + 2x3 = 10 3x1 + 2x2 + x3 = 6 4x1 + 5x2 + 2x3 = 9. Based on these equations, answer the questions below. (a) From the given linear equations, identify the matrices A, x and b such that the linear system can be expressed as a matrix equation. (b) Examine if the matrix A has any pivoting problem? Explain why or why not? (c) Write down the Augmented matrix, Aug (A), from the given linear system, and evaluate the upper triangular matrix U. Note that you have to show the row multipliers mi, for each step as necessary. (d) Using the upper triangular matrix found in the previous question, compute the solution of the given linear system by Gaussian elimination method.
Transcribed Image Text:A linear system is described by the following equations: 6x2 + 2x3 = 10 3x1 + 2x2 + x3 = 6 4x1 + 5x2 + 2x3 = 9. Based on these equations, answer the questions below. (a) From the given linear equations, identify the matrices A, x and b such that the linear system can be expressed as a matrix equation. (b) Examine if the matrix A has any pivoting problem? Explain why or why not? (c) Write down the Augmented matrix, Aug (A), from the given linear system, and evaluate the upper triangular matrix U. Note that you have to show the row multipliers mi, for each step as necessary. (d) Using the upper triangular matrix found in the previous question, compute the solution of the given linear system by Gaussian elimination method.
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