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Linear Algebra With Applications
Found in: Page 276
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Does the following matrix have an LU factorization? See Exercises 2.4.90 and 2.4.93.


Yes, the given matrix does have an LU factorization.

See the step by step solution

Step by Step Solution

Step 1: Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m×n.”

Step 2: Given. 

Given matrix,


Step 3: To find the given matrix is LU factorization or not. 

As seen from Exercise 2.4.93.c, an n×n matrix has an LU factorization if all of its principal sub matrices are invertible.

We have,


To solve,


Since, all of its principal sub matrices A are invertible.

Thus, A does have an LU factorization.

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