Example 2 (a) Determine the LU factorization for matrix A in the linear system Ax = b, where1.1 012.1-11and b=3-1-12.-131(b) Then use the factorization to solve the systemX + x2+ 3x4 = 8,%3D2x1 + x2 - X3 + X4 = 7,3x1 - x2 - X3 + 2x4 = 14,-xI + 2x2 + 3x3 - x4 = -7.

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Example 2 (a) Determine the LU factorization for matrix A in the linear system Ax = b, where 1 1 3 -1 1 and be 3 -1 2 -1 -1 1 2 3 4 (b) Then use the factorization to solve the system X + x2 + 3x4 8, 2x1 + x2 - X3 + X4 = 7, 3x1 - X2 - X3 + 2x4 = 14, -XI + 2x2 + 3x3 - x4 = -7.

Example 2 (a) Determine the LU factorization for matrix A in the linear system Ax = b, where 1 1 3 -1 1 and be 3 -1 2 -1 -1 1 2 3 4 (b) Then use the factorization to solve the system X + x2 + 3x4 8, 2x1 + x2 - X3 + X4 = 7, 3x1 - X2 - X3 + 2x4 = 14, -XI + 2x2 + 3x3 - x4 = -7.

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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Question

Example 2 (a) Determine the LU factorization for matrix A in the linear system Ax = b, where
1.
1 0
1
2.
1
-1
1
and b=
3
-1
-1
2.
-1
3
1
(b) Then use the factorization to solve the system
X + x2
+ 3x4 = 8,
%3D
2x1 + x2 - X3 + X4 = 7,
3x1 - x2 - X3 + 2x4 = 14,
-xI + 2x2 + 3x3 - x4 = -7.

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