The only way I can think of is to show they have the same characteristic polynomial; thus they have the same eigenvalues, But the question asked not to use determinants.
The only way I can think of is to show they have the same characteristic polynomial;...
Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) (Hint: If you consider characteristic polynomial of the matrix then this is an algebra problem) one real eigenvalue and two complex eigenvalues. two real eigenvalues and one complex eigenvalue. three eigenvalues, all of them real. three eigenvalues, all of them complex. only two eigenvalues, both of them real. only one eigenvalue -- a complex one. only two eigenvalues, both of them complex only one...
4. (Extra credit, all hand work. Use your paper and attach.) Let A-and assume a,b,ct are positivs. 0 b c (a) Let f) denote the characteristic polynomial of A. Calculate it and show work. You should get (b) Prove that A has only one real eigenvalue, that it is positive, and that the other two eigenvalues of A must be conjugate complex numbers. Let eigenvalues. λ denote the real positive eigenvalue and let λ2 and λ3 denote the other two...
Let u and v be the vectors shown in the figure to the right, and suppose u and v are eigenvectors of a 2 x2 matrix A that correspond to eigenvalues -2 and 3, respectively. Let T: R2 R2 be the linear transformation given by T(x)-Ax for each x in R2, and let w-u+v. Plot the vectors T(u), T(v), and T(w). 2- u -2 2 4 -2 10- T(v) T(w -10 10 T(u) -10- Ay 10- T(v) T(w) T(u) 10...
Please show all work so I can gain a better understanding. Thank you! (Let X ⊂ R n be non-empty and let A be an n×n matrix. Show that A[co (X)] = co (A[X]). Here co means convex hull.) Exercise 17: Let X C Rn be non-empty and let A be an n × n matrix. Show that Alco (X)-co (A Here co means convex hull. ) Exercise 17: Let X C Rn be non-empty and let A be an...
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
Discuss: Many athletes, both professional and weekend, think that the only way for them to meet protein needs is to consume meat, chicken and other animal protein sources. Using the information that you have learned about protein what do you think? Is it true that athletes have to consume meat? Please make sure that you support your responses with facts. Give examples of complimentary proteins. You can use resources other than the book to support your response but make sure...
We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate pairs). But how can we get the same conclusion by just considering the end behavior of an odd-degree polynomial?Hint: Think about how the root(s) of a polynomial show up on its graph. Then, look at what we know about the end behavior of an...
vectors pure and applied. exercise 6.4.2 OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with respect to some basis. Then β would have Proof Suppose t matrix representation D=(d, 0 say, with respect to that basis and ß2 would have matrix representation 2 (d2 0 with respect to that basis. However for all xj, so β-0 and β2...
I just need help with question 4 only: Consider the RLC circuit where R = 5, C = 1, L = 4 and Vs = 8. 1. Use circuit analysis laws to show that the resistor's voltage and induc- tor's voltage can be modelled as the system of ODEs VR 0 R RC L 2. Solve the eigenvalues and eigenvectors of the coefficient matrix in the system of ODEs. 3. Verify your answer for question (2) by using the eig...
I only need help with d, e, and f. Can you please explain especially d in detail? Thank you 1. Here you will prove the famous identity that 1 1 1 3+5+7+ Do not use the Ratio Test anywhere in this question. (a) Express h as a power series centered at 0. Determine its interval of convergence. Hint: This should be short. (b) Let S(:) be the Taylor series of arctan x at 0. Without computing S(2), briefly explain why...