Answered: Compute the summation of each column of…

Compute the summation of each column of matrix A. Create the above matrix using the MATLAB functions (zeros, ones, eye). Find the determinant and inverse of matrix A.

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter13: Structures

Section: Chapter Questions

Problem 4PP

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Consider the following problem. INPUT: Positive integers r1, ··· , rn and c1, ··· , cn . OUTPUT: An n by n matrix A with 0/1 entries such that for all i the sum of the ith row in A is ri and the sum of the ith column in A is ci , if such a matrix exists. Think of the problem this way. You want to put pawns on an n by n chessboard so that the ith row has ri pawns and the ith column has ci pawns. Consider the following greedy algorithm that constructs A row by row. Assume that the first i-1 rows have been constructed. Let aj be the number of 10 s in the jth column in the first i-1 rows. Now the ri columns with with maximum cj -aj are assigned 1’s in row i, and the rest of the columns are assigned 00 s. That is, the columns that still needs the most 1’s are given 1’s. Formally prove that this algorithm is correct using an exchange argument.
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Consider the matrix multiplication C = AB. A matrix W is called a witness matrix with the following conditions: • If ci j = 0, then wi j = 0.• If ci j = 1, then wi j = k where aik = bkj = 1. make code to displays two Booelan matrices A and B and their productC. Note that we define these matrices with 0 and 1 entries and declare their typesas boolean with dtype = bool statement after specifying the entries. Alternatively,we could have specified theses matrices with True and False entries. The booleanproduct C is then converted to integer by the astype method and both forms of Care printed
I am having trouble with a individual coding problem I am doing in python: Ar = int(input("How many rows does your matrix have? "))Ac = int(input("How many columns does your matrix have? ")) win = GraphWin('Matrix A', 300,300) win.setBackground('white') for p in range(Ac):y = 75 + 40*pfor q in range(Ac):x = 50 + 50*qinputText = Entry(Point(x,y), 3)inputText.setText('0')inputText.draw(win) ## The issue I having is that I want to be able to get the users inputs from their entries so that I can do matrix operations on them. However, anytime I try to append their entries at best I just get their last entry repeated (n)(m) times. I would be very thankful if you can show me how I can change my code so that I append all user entries correctly.
Generate random matrices of size n × n where n = 100, 200, . . . , 1000.Also generate a random b ∈ Rnfor each case. Each number must beof the form m.dddd (Example : 4.5444) which means it has 5 Significant digits in total. Perform Gaussian elimination with and withoutpartial pivoting for each n value (10 cases) above. Report the numberof additions, divisions and multiplications for each case in the form ofa table. No need of the code and the matrices / vectors. Deliverable(s): Two tabular columns indicating the number of additions, multiplications and divisions for each value of n, for with andwithout pivoting in Python
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I do not understand this expression. so is c[i][j] += a[i][h] * b[h][j] mean c[i][j] = a[i][h] * b[h][j] + c[i][j]?? ; We do not know about the + matrix c right?
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(20pts) Consider the matrixA =−2 11−10 5(a) Determine, by hand, an SVD of A, A = UΣVT. The SVD is not unique,so find the one with the minimum number of minus signs in U and V . List thesingular values σ1 and σ2, and the left and right singular vectors.(b) Find A−1 not directly, but via the SVD. Check your result by typing inv(A)in MATLAB or calculating A−1 by other methods.(c) Find the eigenvalues λ1 and λ2 of A. Verify that detA = λ1λ2 and |detA| =σ1σ2
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