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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need ans for part c and d only
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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