The 0 A 2x2 mamix smallest value A² has eigenvalues e lis & el 16 of...
a) Find the eigenvalues and the eigenvectors of the 2x2 matrix: [4 2] [3 -1] b) Solve the initial value problem: dx/dt = 4x + 2y dy/dt = 3x - y with x(0) = 0, y(0) = 7
QUESTION 18 The 2 x 2 matrix A= has complex eigenvalues r = -2£i. An eigenvector corresponding 2 to r = -2+ i is 1-) The system x' = Ax+ (). e-2t has one solution given by x(t) = (2) e-2t. What is the general solution to the system? C1 cost sint - cost 6) -27 +02 e sint sint - cost :) -21 e + (1) e OB C1 cost cost 0-2t + C2 0 sint e-2t + (1)...
e TOnSWing array: intl] a- 1,3,5,7,9,11 (2x2 marks) What is the value stored in the variable total when the followings loops complete? Assume there are ho errors in the code. Assume the loops are independent (L.e., part b is not affected by part a). a) int total-0 f total-total + alil: b) int total = 0; for (inti-l; i<5; i+-2) total total + afi]i
(1 point) Determine the values of a (eigenvalues) for which the boundary-value problem y + y = 0, 0 < x < 8 y(0) = 0, y'(8) = 0 has a non-trivial solution. = an ((2n-1)^2pi^2)/256 ,n= 1, 2, 3, ... Your formula should give the eigenvalues in increasing order. The eigenfunctions to the eigenvalue an are Yn = Cn* sin ((2n-1) pi n/16) where Cn is an arbitrary cons
QUESTION 7 Escriba la tabla inicial simplex e indique cual es el pivote para el siguiente problema de programación lineal: Maximizar, z = 2x2 + x2 Sujeto a: Xy + 4x2 s 2 - 4x +5x2 <16 5x, si *; + 2x, 53 x; 20,x220 a.-2 b.1 C.-4 d.5
The 2 x 2 matrix A -3 2 -1 -1) has complex eigenvalues r = -2+i. An eigenvector corresponding to r = -2+i is The system x' = Ax+ -24 e- has one solution given by x(t) = (2) e-2t. What is the general solution to the system? OA -20 cost sint - cost st) + C2 sint sint - cost e-2t + (1). e-27 och cost e-24 + C3 (2 ) e-24 cost * (sin e tez (-sind) e...
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and corresponding eigenvectors vand v- 1? a. is a 2x2 matrix with repeated eigenvalue λ = 0 with defect 1 (has only one linearly independent eigenvector, not two.) and corresponding eigenvector vi- 13 (5 pts) Which of the direction fields corresponds to the system x -Cx, where...
(1 point) Determine the values of (eigenvalues) for which the boundary-value problem g” + y = 0, 0 < x < 4 y(0) = 0, y' (4) = 0 has a non-trivial solution. An = a , n=1,2,3,... Your formula should give the eigenvalues in increasing order. The eigenfunctions to the eigenvalue in are Yn = Cn* sin(n*pi/2*x) where On is an arbitrary constant.
(1 point) The matrix -1 -1 01 A = -16 0 Lk 0 has three distinct real eigenvalues if and only if -17.036 <k< 29.184
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y'' + xy' + λy = 0, y(1) = 0, y'(e) = 0 λn = n = 1, 2, 3, yn(x) = n = 1, 2, 3,