Answered: Show that the elimination method of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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Question

Show that the elimination method of computing
the value of the determinant of an n × n matrix
involves [n(n − 1)(2n − 1)]/6 additions and
[(n − 1)(n2 + n + 3)]/3 multiplications and divisions.
Hint: At the ith step of the reduction process,
it takes n − i divisions to calculate the multiples
of the ith row that are to be subtracted from the
remaining rows below the pivot. We must then calculate
new values for the (n − i)2 entries in rows
i + 1 through n and columns i + 1 through n.

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