These problems start with a bidiagonal n by n backward difference matrix D = I - S. Two tridiagonal second difference matrices are DDT and A =-S+21 - ST. The shift S has one nonzero subdiagonal Sii-1 = 1 for i = 2,...,n. A has diagonals –1,2, -1. 2 Show that the inverse of D = I- S is D-l = lower triangular "sum matrix" of l's. DD- = I is like the Fundamental Theorem of Calculus: derivative of integral of f equals f. Multiply (D-)T times D- to find (DDT)-1 for n = 4.

These problems start with a bidiagonal n by n backward difference matrix D = I - S. Two tridiagonal second difference matrices are DDT and A =-S+21 - ST. The shift S has one nonzero subdiagonal Sii-1 = 1 for i = 2,...,n. A has diagonals –1,2, -1. 2 Show that the inverse of D = I- S is D-l = lower triangular "sum matrix" of l's. DD- = I is like the Fundamental Theorem of Calculus: derivative of integral of f equals f. Multiply (D-)T times D- to find (DDT)-1 for n = 4.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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Similar questions

Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be used to create a leading 1 at the top of the first column. Which do you prefer and why?
If A and B are matrices with the same dimension and k is a real number, how do you find A+B and kA ?

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