Chapter 6, Section 6.5, Question 07
Chapter 6, Section 6.5, Question 07 Consider the given system of equations. 10-1 (a) Find a funda...
Chapter 6, Section 6.5, Question 06 Consider the given system of equations. (a) Find a fundamental matrix Express X (t) as a 2x2 matrix of the form x(t) = where vi-Ci ) s the eigen vector associated with the complex eigen value λί V11 Re (eht vi lm (e,%) Click here to enter or edit your answer (b) Find the fundamental matrix eAr (b) Find the fundamental matrix eAr Click here to enter or edit your answer Click if you...
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental matrix for the given system of equations. Use the eigenvectors so that the coefficeints in the first row all equal 1 Equation Editor Ω Common Matrix Ψ (t) = (b) Find the fundamental matrix重(t) satisfying重(0) = 1. Equation Editor Ω Common Matrix tan a) sin(a) 0os(a) 重(t) = Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental...
Chapter 8, Section 8.5, Question 07 x Incorrect Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect to the basis B . T:R2 R2 is defined by X1- 2x2 X1 T X2 -X2 B = u1, u2} and B = {v1, V2}, where 2 1 V1 = u2 = 1 1 Give exact answer. Write the elements of the matrix in the form of a simple...
Chapter 3, Section 3.2, Question 07 (a) State whether the given system is autonomous or nonautonomous and also whether it is homogeneous or nonhomogeneous. x' x+y11, y = -31x+ sin (t) y The given system is (b) Write the system using matrix notation. ()-) = P +g where [Enter as 2x2 matrix.] P = [Enter as 2x1 matrix. g Chapter 3, Section 3.2, Question 07 (a) State whether the given system is autonomous or nonautonomous and also whether it is...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
Chapter 7, Section 7.8, Question 010 Find the general solution of the given system of equations. X= 6 1) X -25 16 X-C 111 + C2 111 X=1 + 2 <= [(5)2 + (). X-Cil te 111 + C2 , 11t+cal X=1 + cz[(5)*e*** (9)e XC 11t+C2 Itellt 5
need help i only have 15mins left :( Chapter 9, Section 9.7, Question 023 Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = 20, and then find the oth Taylor polynomial for the function in sigma notation In(x) = 1 (If any of your answers contain a factorial, please enter its numerical value. For example, enter 120" instead of "5!". Pa) Edit P.) ? Edit ? Edit Edit P.) = 2 Edit Edit Click if...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
Chapter 13, Section 13.7, Question 023 Find two unit vectors that are normal to the given surface at the point P. V*1 =?:P6,5,1) 1 1 15 1 1 1 U1 = j k and U2 = 15 -k /227 j + 227 227 V227 V227 227 1 1 1 1 ui = 15 k and U2 227 i + 227 j + 227 227 227 15 -k V227 15 -k 227 1 1 1 ui 15 k and u2 =...
Question 7. (15 marks] Consider the discrete time system given by the state equation 07 x4 + 11-18 8/11 - 10/n VIK) = 10 11 **) 1. [3 marks) Determine if the system is (a) Lyapunov state, syptereally ) Bounded input Bounded Output (BIBO) stable. Provide brief explanations 2. (8 marks) Design a discrete-time state feedback control law of the form - Kxkl by finding the gain K to place the closed-loop eigenvalues at 0.5 3. [4 marks) Suppose the...