HomeworkLib
Question

Question 5 Suppose that A is the matrix (51 -1 A= 0 4 0 1 1 3 (a) Find an invertible matrix P such that P-1AP = J where J is

math   Advanced-Math   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

# 15 1 1 1 A-lo u o li i 3) 1 A-dil= 0 15- 01-11 1 1 1 3- . (5-d) (4-2) (3-2) + 1 (4-2) = 0 (4-2) I 22 -82 +15+1] = 0 (und) ((und) (2-4 = 0 d= 4,4,4 A for d = 4 (A-dI) x = 0 15-4 - 1 o 4-4 | My 1 1 3-4 lug Mit - Uz = 0 IO AM = GM= 3 of d= 4 Palol PAPo The vector corresponding to the 4t will be of long tim behaviour. - Take Cz = C₂ = 0 Now, f(t)=c, e g (t) = ci e Altc 462)

0 0
Add a comment
Know the answer?
Add Answer to:
Question 5 Suppose that A is the matrix (51 -1 A= 0 4 0 1 1...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • (a) Find the eigenvalues of the matrix 4) 2 1' and find an eigenvector corresponding to each eigenvalue. Hence find an invertible matrix, P, and a diagonal matrix, D, such that P-1AP = D. (b) Use...

    (a) Find the eigenvalues of the matrix 4) 2 1' and find an eigenvector corresponding to each eigenvalue. Hence find an invertible matrix, P, and a diagonal matrix, D, such that P-1AP = D. (b) Use your result from (a) to find the functions f(t) and g(t) such that f(t)-f(t) +2g(t) g(t) 2f(t) g(t), where f(0)-1 and g(0)-2 (c) Now suppose that f(0)-α and g(0) β. Determine the condition(s) on α and β that must hold if, as t,t is...

  • Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential...

    Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...

  • Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential...

    Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...

  • (1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a gen...

    (1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)- (1 point) Consider the initial value problem -51เซี. -4 มี(0)...

  • (1 point) Diagonalize the matrix 8 8 5 A= 7 7 -7 0 0 3 Namely,...

    (1 point) Diagonalize the matrix 8 8 5 A= 7 7 -7 0 0 3 Namely, find an invertible matrix P and a diagonal matrix D such that P-1AP = D. P= O 0 D = 0 0 0 0

  • A) B) (1 point) The matrix A= 1-3 0 [1 0 -4 0 -1] 0 -5...

    A) B) (1 point) The matrix A= 1-3 0 [1 0 -4 0 -1] 0 -5 has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace. The eigenvalue is -4 A basis for the eigenspace is (1 point) Find the solution to the linear system of differential equations x' y' = = 25x + 727 9 -9.2 – 26y satisfying the initial conditions x(0) = -18 and y(0) = 7. x(t) = y(t) =

  • 3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are...

    3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are given that the characteristic polynomial of A is XA (z) = (z 2). Find the Jordan form J of A and find a matrix P such that P-1AP J. (You do not need to find P-1.) (You may use an online RREF calculator, but remember you only have an ordinary calculator in the exams.)

  • 4. Suppose the matrix equation Az(t) =#(ty has the property that /2 0 0 D =0...

    4. Suppose the matrix equation Az(t) =#(ty has the property that /2 0 0 D =0 1 0 (0 0 -7, and a change of basis matrix given by T 1 1 P = 1 e 1 Compute the solution f(t), and write down the n-th order differential equation associated to the matrix A 4. Suppose the matrix equation Az(t) =#(ty has the property that /2 0 0 D =0 1 0 (0 0 -7, and a change of basis...

  • Let D(p) = 4-p and S(p) = 1 + p. Using the method of linear first-order...

    Let D(p) = 4-p and S(p) = 1 + p. Using the method of linear first-order differential equations, find a general solution to p(t) (it will involve k). What is the long term behaviour of the price? Does it tend to a specific value regardless of the initial price?

  • (1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2...

    (1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT