Question

6.) Use Matlab or another software program to calculate the following. a. Let A=.1.2.3.4;.4.3.2.1;.3.1.4.2;.2.4.1.3. Find A^10000. b. Let B=.1.2.3.4;.4.3.2.1;.3.1.4.2;.2.4.1.29. Find B^10000. C. Let C=[.1.2.3.4;.4.3.2.1;.3.1.4.2;.2.4.1.31]. Find C^10000. d. Comment on the differences between A, B and C. What is the sum of the entries in each row of A,B and C? What is the sum of the entries in each column of A, B and C? e. Comment on the differences between A^10000, B^10000, and C^10000. How large are the entries of each? Draw analogies to 1^10000 for A and 910000 for B and 1.110000 for C.

Answer 1

MATLAB Code:

close all
clear
clc

A = [0.1 0.2 0.3 0.4; 0.4 0.3 0.2 0.1; 0.3 0.1 0.4 0.2; 0.2 0.4 0.1 0.3];
B = [0.1 0.2 0.3 0.4; 0.4 0.3 0.2 0.1; 0.3 0.1 0.4 0.2; 0.2 0.4 0.1 0.29];
C = [0.1 0.2 0.3 0.4; 0.4 0.3 0.2 0.1; 0.3 0.1 0.4 0.2; 0.2 0.4 0.1 0.31];

fprintf('Part (a)\n----------------------------------------\n')
disp(A^10000)

fprintf('\nPart (b)\n----------------------------------------\n')
disp(B^10000)

fprintf('\nPart (c)\n----------------------------------------\n')
disp(C^10000)

fprintf('\nPart (d)\n----------------------------------------\n')
fprintf('The only difference between A, B and C is the last element.\n')
fprintf('Elements of B^10000 are much less than that of A^100000,\n')
fprintf('and the elements of C^10000 are much larger than that of A^100000.\n')

fprintf('\nSum of the entries of each row of A:\n')
for i = 1:size(A,1)
fprintf('\t%.4f\n', sum(A(i,:)))
end

fprintf('Sum of the entries of each row of B:\n')
for i = 1:size(B,1)
fprintf('\t%.4f\n', sum(B(i,:)))
end

fprintf('Sum of the entries of each row of C:\n')
for i = 1:size(C,1)
fprintf('\t%.4f\n', sum(C(i,:)))
end

fprintf('Sum of the entries of each column of A:\n')
for i = 1:size(A,2)
fprintf('\t%.4f', sum(A(:,i)))
end

fprintf('\nSum of the entries of each column of B:\n')
for i = 1:size(B,2)
fprintf('\t%.4f', sum(B(:,i)))
end

fprintf('\nSum of the entries of each column of C:\n')
for i = 1:size(C,2)
fprintf('\t%.4f', sum(C(:,i)))
end
fprintf('\n')

Output:

Command Window Part (a) 0.2500 0.2500 0.2500 0.2500 0.250 0.2500 0.2500 0.2500 0.250 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 Part (b) 1.De-11 * 0.4101 0.4112 0.4108 0.4065 0.4092 0.4103 0.4098 0.4056 0.4108 0.4858 0.41190.4069 0.4114 0.4065 0.4071 0.4022 Part (c) 1.Be+10 * 2.11212.1169 2.1062 2.1110 2.1986 2.1133 2.1310 2.1358 2.1086 2.1027 2.1051 2. 1275 2.1346 2.1287 2.1310 2.1537 Part (d) The only difference between A, B and C is the last element. Elements of B^10000 are much less than that of A 100000, and the elements of C^10000 are much larger than that of A^100000. Sum of the entries of each row of A: 1.0000 1.0000 1.0000 1.0000 Sum of the entries of each row of B: 1.0000 1.0000 1.0000 0.9900 Sum of the entries of each row of C: 1.0000 1.2000 1.0000 1.0100 Sum of the entries of each column of A: 1.0000 1.000 1.000 1.eeee Sum of the entries of each column of B: 1.0000 1.0000 1.0000 0.9900 Sum of the entries of each column of C: 1.0000 1.0000 1.0000 1.0100 fx »