2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. - + 3r, - 213 + 4x, = 0 4r + 12r2 + 7z3 – 14x4 = -1 I - 3r, + 4r, – 8r, = 2 21 – 6x2 + x3 - 2r4 = -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 14 -1 1 -2 2 7 A = 1 0 3 -1 2 -3 -5 i. Find an LU-factorization of A. ii. Use these L and U to solve the system Ax = b, where x = and (c) Find A-. Use A-' to solve the system Ax = b, where A, x and b are the same as given in 2(b).
2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination process. - + 3r, - 213 + 4x, = 0 4r + 12r2 + 7z3 – 14x4 = -1 I - 3r, + 4r, – 8r, = 2 21 – 6x2 + x3 - 2r4 = -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 14 -1 1 -2 2 7 A = 1 0 3 -1 2 -3 -5 i. Find an LU-factorization of A. ii. Use these L and U to solve the system Ax = b, where x = and (c) Find A-. Use A-' to solve the system Ax = b, where A, x and b are the same as given in 2(b).
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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Transcribed Image Text:2. (a) Solve the following system of linear equations by using Gauss-Jordan elimination
process.
-z + 3r2 - 213 + 4x4 = 0
4r1 + 12r2 + 7x3 = 14.x4 = -1
I1 = 3r2 + 4r3 - 8r4 = 2
211 – 6r2 + x3 – 2:r4 = -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
14 -1
1 -2
10 3
-1 2 -3 -5
-3
2 7
A =
i. Find an LU-factorization of A.
ii. Use these L and U to solve the system Ax = b, where x =
and
b =
(c) Find A-. Use A- to solve the system Ax = b, where A, x and b are the same as
given in 2(b).
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