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.
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.
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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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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