Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter D.2, Problem 8E
Program Plan Intro
To prove,
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Determine the value(s) of x so that the matrix below is the augmented matrixof an inconsistent linear system.
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If there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A, n x n square matrix is diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues of the matrix A.
A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) :
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-1
1
3
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a)Write a program that calculates the eigenvalues and eigenvectors of matrix A using NumPy.
b)Write the program that determines whether the D matrix is diagonal by calculating the D matrix, using NumPy.
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Verify that the full perspective to canonical matrix Mprojection takes (r, t, n) to (1, 1, 1).
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- Certain numerical stability issues have not been considered in this section. Throughout, it has beenassumed that either an exact inverse of A exists, or that the inverse of A does not exist. That is, theelements{Perform Gaussian elimination to transform A into an upper-triangular matrix.}arrow_forwardsubject : analysis of algorithm Q.No.1: Consider the following chain of matrices having matrices A, B, C and D. You have to consider the digits of your Registration Number in the order of the matrix as given. Add 2 to the digit if its zero. For example, your Reg_No. 19-Arid-797 has last digit 7, 2nd last digit 9 and 3rd last digit 7. A B C 2 X last digit last digit X 2nd last digit 2nd last digit X 3nd last digit D 3rd Last digit X 4 What will be the minimum number of multiplication to multiply these matrices? Show the order of multiplication as well.arrow_forwardmake an adjacency matrix for the following: E= {(1,2),(2,1),(3,2),(4,3),(4,5),(5,6),(6,7)}arrow_forward
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