An times n is called a band matrix if aij = 0 whenever | i
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Antimes n is called a band matrix if aij whenever i j w for
some positive integer w called the bandwidth. In other words, the
nonzero entries of A are constrained to be in a band of w diagonal lines
above and below the main diagonal. For example, tridiagonal matrices
have bandwidth one, and diagonal matrices have bandwidth zero. If
A is a nonsingular matrix with bandwidth w and if A has an LU
factorization A LU then L inherits the lower band structure of A
and U inherits the upper band structure in the sense that L has lower
bandwidth w and U has upper bandwidth w Illustrate why this
is true by using a generic times matrix with a bandwidth of w
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