Problem 2 Comment for Problem 2: You are welcome to check your work with a numer

Question

Problem 2 Comment for Problem 2: You are welcome to check your work with a numerical analysis program such as Matlab, but to receive credit for these simple problems you should do them by hand and show all your work. Thank you! a). For the matrix 0 -12 Compute the eigenvalues (A , 2, and their associated unit mag- nitude eigenvectors (Ly-2, and ts). (Recall goes with , and so on). Compute the eigenvalues i) by direct expansion of the eigenvalue polyno- mal (you should get a polynomial in , which you then factor), and ii) by a factored mlatrix-of-minors determinant approach (you should get ( times a second order polynomial in ). b). Do the same thing as in part (a) for the matrix 2 0 -1 0 2 c). What can you say about the eigenvalue/eigenvector solution when one of the diagonal elements is nonzero and its associated off-diagonal row and column elements are zero? (The cases in parts (a) and (b))? d). Now solve the eigenvalues and eigenvectors for the matrix 2 -1 0 using just the second approach (factored matrix-of-minors

Explanation / Answer

Calculating charactersitic polynomial of type de|A- k I |=0

One factor will (1-k)((2-k)2-1)=0 which is equal to

(1-k)(3-k)(1-k)=0 hence eigen values are equal to 1, 3, 1.

Now corresponding eigenvectors are for k=1 we have (1,0,0)T and 1/sqrt(2).(0,1,1)T.

And k=3 is 1/sqrt(2)(0,1,-1)t.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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