Recalling that the (i, j)-entry of the matrix CCT is given byΣ1

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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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The matrix M represents a linear transformation of two-dimensional space and det(M) = 2. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation? The area of the region is one-half as large.The area of the region is one-third as large. The area of the region triples.The area of the region doubles. The linear transformation T sends all of three-dimensional space to a line. What can you say about the value of the determinant of the matrix representing the transformation? The determinant is negative.The determinant is 0. The absolute value of the determinant is less than 1.
(1) A directed graph G is defined with the following adjacency matrix. Label the nodes of G as 1,2,3, 4 and plot G. (1 0 0 1 0 100 0 010 1001, (2) Let f(x) = x* + (-2)x² + 3x + 4. Re-write f(x) in the telescoping form that can be used in Horner's method.
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G.6
Let G be the graph shown. 3 5 2 Q The adjacency matrix is (use the vertex labels for the row and column numbers)
A sheet has vectors m = [1 1]T and n = [4 0]T . It is stretched, making m become p = [1 4]T and n become q = [4 1] T. If the stretching process is described by a linear transformation, what is the matrix A for this process?
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Home work Q: Find the minimum poynomial for the following matrices. Is A diagonali zable -2 2 -3 1- A = 2 - A 2 -6 -1 -2 -2
Consider the COO format of a sparse matrix A: A. data = [0.40 0.10 0.30 0.70 0.10 0.20 0.70 0.80] A.row = [2 0 3 0 0 1 2 2] A. col = [02 2 3 0 3 0 2 3] Construct the matrix A from the COO format.
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Recalling that the (i, j)-entry of the matrix CCT is given by Σ 1