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2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. -11 + 3x2 – 2rz + 4.x4 4.x1 + 12x2 + 7.r3 – 14x4 -1 I1 – 3r2 + 4x3 – 8x4 2 2.r1 – 6r2 + 13 – 214 -3. Write the solution in column form by explicitly isolating the parameter(s) associated with free variable(s), if there is any.

2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. -11 + 3x2 – 2rz + 4.x4 4.x1 + 12x2 + 7.r3 – 14x4 -1 I1 – 3r2 + 4x3 – 8x4 2 2.r1 – 6r2 + 13 – 214 -3. Write the solution in column form by explicitly isolating the parameter(s) associated with free variable(s), if there is any.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3BEXP
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2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. -x1 + 3x2 – 2.x3 + 4x4 = 0 4.x1 + 12r, + 7r3 – 14x4 -1 I1 – 3r2 + 4x3 – 874 2x1 – 6x2 + x3 – 2.74 2 -3. Write the solution in column form by explicitly isolating the parameter(s) associated with free variable(s), if there is any. (b) Consider the following matrix 1 4 -1 2 7 1 -2 A = 1 0 3 -3 -5 i. Find an LU-factorization of A. ii. Use these L and U to solve the system Ax = b, where x = and I3 1 7 b = 5 (c) Find A-1. Use A-1 to solve the system Ax = b, where A, x and b are the same as given in 2(b).
Transcribed Image Text:2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. -x1 + 3x2 – 2.x3 + 4x4 = 0 4.x1 + 12r, + 7r3 – 14x4 -1 I1 – 3r2 + 4x3 – 874 2x1 – 6x2 + x3 – 2.74 2 -3. Write the solution in column form by explicitly isolating the parameter(s) associated with free variable(s), if there is any. (b) Consider the following matrix 1 4 -1 2 7 1 -2 A = 1 0 3 -3 -5 i. Find an LU-factorization of A. ii. Use these L and U to solve the system Ax = b, where x = and I3 1 7 b = 5 (c) Find A-1. Use A-1 to solve the system Ax = b, where A, x and b are the same as given in 2(b).
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