Solve Find the eigenvalue and eigenvectors of A (hint: type eig in the command S

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Find the eigenvalue and eigenvectors of A (hint: type eig in the command Show that the trace of A is the sum of all the eigenvalues (Hint: the difference must be zero) let EV = sum of all eigenvalues % let TR = trace of A. Define an upper (or lower triangular matrix) called B that is 3x3. Find the eigenvalues and eigenvectors of B without using the eig function. (Hint use property 3 on page 191). let LI, L2 and L3 be the % three eigenvalues. verify your finding by using the eig function. (Hint you could use the sort function to compare the two vectors). Find the determinant of B by using the the eigenvalues. Find the determinant of B by using the the eigenvalues. Find the determinant of B by using the function in Matlab verify that the determinant of B found with both methods is the same % (hint: difference must be zero) detB_method1 = detB_method2 = diff section3 =

Explanation / Answer

clc;

%%part1

n=9;

p=9;

A=rand(2,2);

[E D]=eig(A);

EV=sum(sum(D));

TR=sum(trace(A));

diff_section1=EV-TR

%% part2

B=[1 2 3;0 2 4;0 0 6];

% for triangular matrix eigen values are same as diagonal elements

L1=B(1,1);

L2=B(2,2);

L3=B(3,3);

B_eigen=eig(B);

diff_section2=B_eigen-[L1 L2 L3]'

%%PART 3

detB_method1=L1*L2*L3; %PROPERTY OF TRIANGULAR ;DET=MATRIX PRODUCT OF DIAGONAL ELEMENTS

detB_method2=det(B);

diff_section3= detB_method1-detB_method2

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