# MATH 645 UNH Vectors Dot Products & Schwarz Inequality Exercises Exam Practice

I need an explanation for this Algebra question to help me study.

10 problems A band matrix is a square matrix with nonzero entries only on the main diagonal and
on w of the diagonals above and below the main diagonal, and zeros everywhere else. The matrix B
below is an example of a 5×5 symmetric band matrix with w = 1. Elimination for band matrices is
much cheaper than elimination for ordinary matrices. For a generic n × n band matrix B with exactly
w nonzero bands above and below the main diagonal, approximately how many multiplication and
subtraction operations are necessary for elimination B → U?



1 2 0 0 0



2 1 2 0 0


B= 
0 2 1 2 0




0 0 2 1 2


0 0 0 2 1

New York University
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