Question

Alt Print out this page and write answers on the sheet where indicated. Algebra 1. Consider the matrisx 0 -1 2 4 2 -3 6 -9 -12 4 (a) Using Matlab calculate det (B) (b) Solve the system of equations below with LU P decomposition using Matlab. (See SCTA 5.) 22a3 44 +2x5 3 473 -3xī_ 62:2-923-1224 + 4x5 = 1 3-5-3 2. Consider the matrix A = (a) Use Matlab to determine the characteristic polynomial of A. Write your polynomial in the box below (b) Using Matlab solve the characteristic equation (c) Using Matlab find a matrix P and a diagonal matrix D such that P- AP (d) Using (c) and matlab determine A 3. Consider the matrix D 5 6 6 8 2 2 2 8 C 6 6 2 8

Just MATLAB code please

Answer 1

Matlab code LU decomposition and solution clear all close all %&Answering question 1. Matrix B B-l 2 3 4 1:0-1 2 4 2;0 040 0-3-6-9-124;0 0 11 1]; %displaying the matrix fprintf ( Matrix B-In) disp (B) Determinant ofB det_B-det (B) tprint f ("Determinant of is %f"\n", det-B) B %LU decomposition of B %Displaying all matrix fprintf(L matrix-\n disp (L) fprintf('U matrix-\n) disp(U) fprintf ( P matrix-\n) disp (P) %solution vector b-[2 3;4 11 solving the equation fprintf 'Solution Vector is n) disp (x) An swering question 2. A-[1 3 3:-3-5 -3;3 3 1; %displaying the matrix fprintf (Matrix A-n) disp(A) syms x AA-sym (A); polyA charpoly (AA, x); fprintf(Characteristic polynomial is\n') disp (polyA) %solving the polynomial

eigenAsolve (polyA); fprintf( Solution is\n') disp(eigenA) %finding P and D matrix [vec, val]-eig(A) fprintf( 'Matrix P isin') disp (vec) D-inv(vec) A*vec; fprintf( And D matrix is disp (D) D matrix is\n') Finding A 9 A9-vec* (D. 9)inv(vec)i fprintf( Finding A"9=\n') disp (A9) 용욤욤응용욤욤응용욤욤%%욤욤%%욤욤 End of Code 욤욤응용욤욤응용욤욤응용욤욤응용 Matrix B= 2 -9-12 Determinant of B is 28.000000. L matrix- Columns 1 through 3 0. 25 -0.333333333333333 -1.11022302462516e-16 9.71445146547012e-17 Columns 4 through 5 6.66133814775094e-16 U matrix- Columns 1 through 3

2 Columns 4 through 5 -12 2.33333333333333 P matrix- Solution Vector is 8. 00000000000001 Matrix A- Characteristic polynomial is x3 3 x2-4 Solution is Matrix P is -0.577350269189626 -0.787626158614816 0.420644616422049 0.577350269189626 0.207443082528818 -0. 816369814605004 -0.577350269189626 0.580183076085998 0.395725198182954

And D matrix is 6.91797521473434e-16 -2.96596306538106e-16 -3. 72248211441642e-16 5.11760939987911e-16 1.65138893315861e-16 5.45477228410489e-16 Finding A*9- 0.999999999998477 512.999999999997 512.999999999999 -512.999999999997 -1024.99999999999 -512.999999999998 512.999999999998 512.999999999997 0.999999999998868 Published with MATLAB® R2018a

%%Matlab code LU decomposition and solution
clear all
close all

%%Answering question 1.

% Matrix B
B=[1 2 3 4 1;0 -1 2 4 2;0 0 4 0 0;-3 -6 -9 -12 4; 0 0 1 1 1];

%displaying the matrix
fprintf('Matrix B=\n')
disp(B)
%Determinant of B
det_B=det(B);
fprintf('Determinant of B is %f.\n',det_B)

%LU decomposition of B
[L,U,P] = lu(B);
%Displaying all matrix
fprintf('L matrix=\n')
disp(L)

fprintf('U matrix=\n')
disp(U)

fprintf('P matrix=\n')
disp(P)

%solution vector
b=[2;3;4;1;1];

%solving the equation
y = L\(P*b);
x = U\y;

fprintf('Solution Vector is \n')
disp(x)

%%Answering question 2.

A=[1 3 3;-3 -5 -3;3 3 1];

%displaying the matrix
fprintf('Matrix A=\n')
disp(A)

syms x
AA = sym(A);
polyA = charpoly(AA,x);
fprintf('Characteristic polynomial is\n')
disp(polyA)
%solving the polynomial
eigenA = solve(polyA);
fprintf('Solution is\n')
disp(eigenA)

%finding P and D matrix

[vec,val]=eig(A);
fprintf('Matrix P is\n')
disp(vec)

D=inv(vec)*A*vec;
fprintf('And D matrix is\n')
disp(D)

%Finding A^9
A9=vec*(D.^9)*inv(vec);
fprintf('Finding A^9=\n')
disp(A9)

%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%