I need this Linear Algebra and Fourier Analysis course question solve. 2. (a) Solve the following system of linear equations by using Gauss-Jordan eliminationprocess.-*1 + 3x2 – 2rz + 4.r4 = 04.x1 + 12x2 + 7xz - 14x4-1x1 - 3x2 + 4x3 - 8x4%3D2x1 - 6x2 + x3 - 2x4 = -3.Write the solution in column form by explicitly isolating the parameter(s) associatedwith free variable(s), if there is any.(b) Consider the following matrix1 4 -1 -31 -22 71 0-1 2 -3 -5A =3i. Find an LU-factorization of A.12ii. Use these L and U to solve the system Ax b, where x =and1317b =-2(c) Find A-. Use A- to solve the system Ax = b, where A, x and b are the same asgiven in 2(b).

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Answered: 2. (a) Solve the following system of…

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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I need this Linear Algebra and Fourier Analysis course question solve.

2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination
process.
-*1 + 3x2 – 2rz + 4.r4 = 0
4.x1 + 12x2 + 7xz - 14x4
-1
x1 - 3x2 + 4x3 - 8x4
%3D
2x1 - 6x2 + x3 - 2x4 = -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 -3
1 -2
2 7
1 0
-1 2 -3 -5
A =
3
i. Find an LU-factorization of A.
12
ii. Use these L and U to solve the system Ax b, where x =
and
13
1
7
b =
-2
(c) Find A-. Use A- to solve the system Ax = b, where A, x and b are the same as
given in 2(b).

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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