Question

Assume that all the eigenvalues ​​of A have a negative real part. Show that the linear...

Assume that all the eigenvalues ​​of A have a negative real part. Show that the linear system x ̇ = Ax has at least one non-trivial solution x (t) so that
lim x (t) = 0 when t tend to infinite
Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
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
Similar Questions
Suppose A is a 2x2 matrix whose eigenvalues all have negative real parts. For the system...
Suppose A is a 2x2 matrix whose eigenvalues all have negative real parts. For the system x 0 = Ax, is the origin stable or unstable?
For each statement below, either show that the statement is true or give an example showing...
For each statement below, either show that the statement is true or give an example showing that it is false. Assume throughout that A and B are square matrices, unless otherwise specified. (a) If AB = 0 and A ̸= 0, then B = 0. (b) If x is a vector of unknowns, b is a constant column vector, and Ax = b has no solution, then Ax = 0 has no solution. (c) If x is a vector of...
Find particular solution to the non-homogeneous linear system. Explain and show all steps. X' = [...
Find particular solution to the non-homogeneous linear system. Explain and show all steps. X' = [ 0 2 ] X + [ 1 ] (e^t) [ -1 3 ] [ -1 ]
4. Suppose that we have a linear system given in matrix form as Ax = b,...
4. Suppose that we have a linear system given in matrix form as Ax = b, where A is an m×n matrix, b is an m×1 column vector, and x is an n×1 column vector. Suppose also that the n × 1 vector u is a solution to this linear system. Answer parts a. and b. below. a. Suppose that the n × 1 vector h is a solution to the homogeneous linear system Ax=0. Showthenthatthevectory=u+hisasolutiontoAx=b. b. Now, suppose that...
q.1.(a) The following system of linear equations has an infinite number of solutions x+y−25 z=3 x−5 ...
q.1.(a) The following system of linear equations has an infinite number of solutions x+y−25 z=3 x−5 y+165 z=0    4 x−14 y+465 z=3 Solve the system and find the solution in the form x(vector)=ta(vector)+b(vector)→, where t is a free parameter. When you write your solution below, however, only write the part a(vector=⎡⎣⎢ax ay az⎤⎦⎥ as a unit column vector with the first coordinate positive. Write the results accurate to the 3rd decimal place. ax = ay = az =
x1-5x2+x3+3x4=1 2x1-x2-3x3-x4=3 -3x1-3x3+7x3+5x4=k 1 ) There is exactly one real number k for which the system...
x1-5x2+x3+3x4=1 2x1-x2-3x3-x4=3 -3x1-3x3+7x3+5x4=k 1 ) There is exactly one real number k for which the system has at least one solution; determine this k and describe all solutions to the resulting system. 2 ) Do the solutions you found in the previous part form a linear subspace of R4? 3 ) Recall that a least squares solution to the system of equations Ax = b is a vector x minimizing the length |Ax=b| suppose that {x1,x2,x3,x4} = {2,1,1,1} is a...
State why the system of equations must have at least one solution. (Select all that apply.)...
State why the system of equations must have at least one solution. (Select all that apply.) 5x + 5y − z = 0 10x + 5y + 5z = 0 5x + 15y − 15z = 0 Solve the system and determine whether it has exactly one solution or infinitely many solutions. (If the system has an infinite number of solutions, express x, y, z in terms of the parameter t.) (x, y, z) =
Choose either true or false for each statement a. There is a vector [b1 b2] so...
Choose either true or false for each statement a. There is a vector [b1 b2] so that the set of solutions to 1 0 1 0 1 0 [ x1, x2 , x3,] =[b1b2] is the z-axis.   b. The homogeneous system Ax=0 has the trivial solution if and only if the system has at least one free variable. c. If x is a nontrivial solution of Ax=0, then every entry of x is nonzero. d. The equation Ax=b is homogeneous...
Let f(x) be a function that is continuous for all real numbers and assume all the...
Let f(x) be a function that is continuous for all real numbers and assume all the intercepts of f, f' , and f” are given below. Use the information to a) summarize any and all asymptotes, critical numbers, local mins/maxs, PIPs, and inflection points, b) then graph y = f(x) labeling all the pertinent features from part a. f(0) = 1, f(2) = 0, f(4) = 1 f ' (2) = 0, f' (x) < 0 on (−∞, 2), and...
Exercise 2.4 Assume that a system Ax = b of linear equations has at least two...
Exercise 2.4 Assume that a system Ax = b of linear equations has at least two distinct solutions y and z. a. Show that xk = y+k(y−z) is a solution for every k. b. Show that xk = xm implies k = m. [Hint: See Example 2.1.7.] c. Deduce that Ax = b has infinitely many solutions.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT