please answer the last two question please. i really need help and it is for mat

Question

please answer the last two question please. i really need help and it is for matlab.please only help if you know how to do it.

0.5. HOW TOFIND EIGENVALUES AND EIGENVECTORS USING MATLAB9 0.5.1 Does row operation preserve eigenvalues? Let Let B obtained by interchanging the first and second row of A. To obtain B, define the permutation matrix P1 0 0 0 0 1 Enter A, B and P in MATLAB Find B PA ( recall to type P*A in MATLAB) Type: eig(B) to find eigenvalues of B Observe that eigenvalues changed because of the row operation done on the matrix So row operations will change the eigenvalues of a matri>x What is the effect of adding a multiple ofI(identit matrix) to A? 0.5.2 let A6 1 0 Enter A in MATLAB Type: eig(A) Type: A1-A-3*eye(3) Type: eig(Al) Type: A2-A+4*eye(3) Type: eig(A2) Type: A3-A-5*eye(3) Type: eig(A3) Type: A4-A-10*eye(3)

Explanation / Answer

1. Eigen value of matrix will get changed if there is change in matrix's diagonal. Since here we can se that you are required to change matrix by substracting 6 times of Identity matrix. So eigen value will get change after substraction.

Lets use same example as in question, enter Matlab code,

M = [1 2 1;6 -1 0; -1 -2 -1];

eig(M); % You will get answer 3

M1 = M - 6*eye(3);

eig(M1) % You will get answer -3

So from this you can see that eigen value will get changed if there is change in diagonal of matrix.

Formula for eigen value = (Eigen value of M) - 6(Eigen value of Identity matrix) = 3 - 6(1) = -3

2. For generalise term,

if k is an eigen value of M matrix, after that you substract sI from M matrix,

New eigen value = (Eigen value of M) - s(Eigen value of Identity matrix) = k - s(1) = k - s

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.