find a PTLU factorization of the given matrix A. 4- A =-1 2 11 3 3

To find factorization of the given matrix A.

Answered: 4 - A = -1 2 1 1 3 3

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

find a P^TLU factorization of the given matrix A.

Expert Solution

Step 1: Given information:

$A equals open square brackets table row 0 1 4 row cell negative 1 end cell 2 1 row 1 3 3 end table close square brackets$

To find $P to the power of T L U$ factorization of the given matrix A.

Step 2: Using Gauss elimination method.

Using $R subscript 1 left right arrow R subscript 2$

$open square brackets table row cell negative 1 end cell 2 1 row 0 1 4 row 1 3 3 end table close square brackets$

$R subscript 3 rightwards arrow R subscript 3 plus R subscript 1$

$open square brackets table row cell negative 1 end cell 2 1 row 0 1 4 row 0 5 4 end table close square brackets$ $open square brackets L subscript 31 equals negative 1 close square brackets$

$R subscript 3 rightwards arrow R subscript 3 minus 5 R subscript 2$

$open square brackets table row cell negative 1 end cell 2 1 row 0 1 4 row 0 0 cell negative 16 end cell end table close square brackets$ $open square brackets L subscript 32 equals 5 close square brackets$ (Upper triangular matrix)

Thus, $U equals open square brackets table row cell negative 1 end cell 2 1 row 0 1 4 row 0 0 cell negative 16 end cell end table close square brackets$

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