Determine the asymptotic stability of the system x' = Ax, where A is 2x2 matrix, A = alpha beta gamma delta ( that is. first row is alpha beta, second row is gamma delta) if it is known that determinant of A, det(A) = alpha*delta - beta*gamma > 0, and th
Determine the asymptotic stability of the system x' = Ax where A is 3 x 3 matrix A = -1 1 1 0 0 1 0 0 -2 ( first row is -1 1 1 second is 0 0 1 and third is 0 0 -2) More specifically, what stability conclusion(s) can be drawn? ( Justify your answer)
(i) Find eigenvalues and eigenvectors. (ii) Classify the critical point (0, 0) as to type and determine whether it is stable or unstable. (iii) Sketch several trajectories in the phase plane. Please see the attached file for the fully formatted problems.
I could really use your help on the steps and the problem. X' = (1 -1 2 -1 1 0 -1 0 1) X
Find the general solution. X' = (1 0 0 2 2 -1 0 1 0) X
Find the general solution for the following system: dx/dt = 3x - y dy/dt = 9x - 3y
Show your argument in details you can use Maple to assist you in long calculations. YOU CANNOT USE dsolve command! Consider the following system 1) Find the general solution the systems 2) Find the solution that satisfies and . Is the solution unique? 3) Plot a (the) solution of question 2). (See attached
(i) Find eigenvalues and eigenvectors: (ii) Classify the critical point (0,0) as to type and determine whether it is stable or unstable: (iii) Sketch several trajectories in the phase plane. --> =(-7 10) --> x' (-5 8) x
It is known that the time (in hours) between consecutive traffic accidents can be described by the exponential r.v. X with parameter (Lambda = 1/60). Find (i) P(X < or = 60); (ii) P(X> 120); and (iii) P(10<X< or = 100).
1. Let a, b be positive integers, and write a = qb + r, where q, r are Elements of Z and 0 (= or)< r < b. Suppose that d = gcd(a, b). a) If r = 0 show that d = b. b) If r > 0 show that d = gcd(b, r). 4. Use Problem 1 to find: a) gcd(100; 3); b) gcd(100; 82).
1. Let d; a; b; r, and q be integers. a) Suppose that d|a and d|b. Show that d|(ra + qb). b) Suppose a = qb + r. Show that the set of common divisors of a and b is the set of common divisors of b and r.
25 Algebra Problems : Trigonometry, Graphing, Matrices, Simplifying Expressions and Solving Equations
The flow rate V (in cm/s) of a storm drainpipe follows the following expression. Find the value of V when t = 2.500 s. a. 33.56 b. 5.42 c. 132.6 d. 22.5 A boat approached a harbor and the captain takes two bearings to calculate the distance to the harbor. Bearing 1 is read at 0 degrees and bearing 2 is read at 30 de
(See attached file for full problem description with proper equations) --- 9.3-3 Let . Use the result of exercise 4 of Section 9.1 to show that does not converge uniformly on [0,1], even though converges pointwise. ---
Find the least squars solution of Ax=b, retaining five places to the right of the decimal point. Finally, verify that your least squares solution satisfies the least-squares problem and calculate the normalized error e=E/ lbl. A: ( 0 8 -1 ) ( 1 2 0 ) ( 0 0 3 ) ( 0 4 5 ) (represe
Let X be a compact metric space and Y be a normed space. Prove that if f_n belongs to C(X,Y), then lim_n f_n = f_o in the Sup norm if and only if lim_n f_n = f_o uniformly in X. [ Note: Sup norm: ||f|| = Sup||f(x)|| for every x in X.]
Use linear approximation, the tangent line approximation, to approximate the following: (56.4)^(1/3) (64.4)^(1/3) Show processes. Do not use a calculator. Note: the correct answer are different from the calculator computed values
1. The sum of three numbers is 6. The third number is the sum of the first and second numbers. The first number is one more than the thrid number. Find the numbers. 2. Sports - Alexandria High School scored 37 points in a football game. Six points are awarded for each touchdown. After each touchdown, the team can earn
Q: Find the point P on the line passing through both the origin and the point 1,1,1 that is closest to the point 2,4,4. Then find the point q on the line passing through both the origin and the point 2,4,4 that is closes to the point 1,1,1
We've defined the error between a vector b in Euclidean vector space R^m and its projection p onto a subspace of R^m as E=lb-pl. Prove the extended pythagorean Theorem: E^2=lbl^2 - lPl^2.
Consider two vectors a and b with elements a1,a2,a3 and b1,b2,b3 respectivley. Express the projection of b onto a in terms of these elements. Then do the same for the projection of a onto the axis of b.
Solve the system of equations [ 1 1 0 1 8] [ X1] [ 2] [-1 1 2 -1 0] [ X2] [-1] [-2 0 4 6 2] [ X3] = [ 2] [0 -3 -1 1 4 ] [ 0] [X4] [3 1 2 5-1] [ 1] [X5]
I need a counterexample for the following: If f:[a,b] -> R is ONE-TO-ONE and satisfies the intermediate value property, then f is continuous on [a,b]. I know that this is a false statement if you exclude the one-to-one property. The example I received before was f(x) = sin(1/x), but this function is not one-to-one. I am
Two tanks each hold 3 liters of salt water and are connected by two pipes (see figure below) the salt water in each tank is kept well stirred. Pure water flows into tank A at a rate of 5 liters per minute and the salt mixture exits tank B at the same rate. Salt water flows from tank A to tank B at the rate of 9 liters per min
(See attached file for full problem description with diagram) --- Electrical Networks Determine the loop currents in the electrical network shown in the diagram. ---
(See attached file for full problem description with symbols) --- Suppose is a matrix such that defines an element for . Show that . ---
1. Discuss each of the three operations in Gaussian elimination. What do they have in common and how do they help solve systems of linear equations? 2. What is an Eigenvalue? What is an Eigenvector?
1. Why did Leontief use linear algebra techniques to create his model? Can you think of alternative methods? 2. What are the main strengths of his model? 3. Does it have any limitations (that you can think of)? 4. How might the Input-Output model be useful in the real world? (In other words, would anyone except an Economist
I am having a problem drawing the table for the following system: Define a universal set U as the set of counting numbers. Form a new set that contains all possible subsets of U. This new set of subsets together with the operation of set intersection forms a mathematical system. Then I have to tell which properties that we did
In the expansion (a+b)^14 find: a) The coefficient of a^10 b^4. b) The coefficient of a^6 b^8.
(See attached file for full problem description with equations) --- Consider the system: a) Rewrite using matrix notation b) show that the following vectors , Are solutions and they are linearly independent c)write the general solution of the system ---