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Math / Linear Algebra and Its Applications 5 / Chapter 1.2 / Problem 32E

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

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Solved: Suppose an n × (n + 1) matrix is row reduced to

Chapter 1, Problem 32E

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QUESTION:

PROBLEM 32E

Suppose an n × (n + 1) matrix is row reduced to reduced echelon form. Approximately what fraction of the total number of operations (flops) is involved in the backward phase of the reduction when n = 30? when n = 300?

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QUESTION:

PROBLEM 32E

Suppose an n × (n + 1) matrix is row reduced to reduced echelon form. Approximately what fraction of the total number of operations (flops) is involved in the backward phase of the reduction when n = 30? when n = 300?

ANSWER:

Solution

Step 1

In this problem we have to the find the fraction of the total number of operations (flops) in the backward phase of the reduction when $n\ =\ 30$ , $n=300$

For an $n\ ×\ (n\ +\ 1)$ matrix when $n\geq{}30$ the number of flops for getting echelon form is $\frac{2{n}^{3}}{3}$ and the number of flops for getting reduced echelon form is ${n}^{2}$ .

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