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Fill in the blanks. $1+1 SO s+371 To S+1 5+2 Example 1: Find the solution to the initial value problem y" + 3y' + 2y = t satisfying y(0) = 1 and y'(0) = 0. Solution: Step 1: Take the LT of this IVP: (s2Y(s) – sy(0) – y'(0))+3(sY(s) – y(0)) + 2Y(s) = 1! 53 +382 +1 (52 + 35 + 2)(s) – 5 – 3 = which leads to Y(5) s2+3+2 s? (s2+3+2) Step 2: Write Y(s) in...
yours climaniton Qro² QNO O su-3y =37 - 2u tiy--38 192=-5 - 4+ y +262 2 23nt7y +82-13 an Sohne method For exane bu+4y=2 methed 34-sy=-394 Solettlon 6n+4y=2-0 30-s.y =-34 0.5 multiple egi() os (butu) - sut2y +82 (i 3u-5y = 39 34 +2y = 2 & Lois etc continue
3. Consider 2 00 0 0 3 12 A=1-4 3 3-2 -2 21 0 You are given that the characteristic polynomial of A is XA (z) = (z 2). Find the Jordan form J of A and find a matrix P such that P-1AP J. (You do not need to find P-1.) (You may use an online RREF calculator, but remember you only have an ordinary calculator in the exams.)
For each of the following matrices determine whether the matrix is in REF, in RREF or in neither RREF nor REF 0 2 -1 34 010 3 0 B- 00 2-5 0 A-0 0 0 0 0 000 0 1 0 0 0 2 1 0 1 0-4 0 D=100 C-1001 000 0 1 14-17 0 0-2 6 3 00 0 1 4 00 0 0 -3 0 0 1 G- 10 H=1000 0 0 1 J-0 0 1 A...
fill in the blanks. b a d (s+1) S-1 5+1 st-2s +1 Example 3: Find the solution to the 4th order IVP y'' - 2y" + y = 0, y(0) = 1, y'0) = -1, y"0) = 0, and y'" (0)=2. Solution: Step 1: Take the LT of this IVP: (s*Y(s) - sy(0) - say'(0) - sy"(0) - y" (0)) - 2 (s2Y(s) - sy(0) - y'(0)) + Y($) = 0 so (s* – 252 + 1)Y(s) – 53 +52...
1. For each system of linear equation, find the solution by Gaussian (set up the augment matrix, forward elimination to find REF, back substitution to find solution) b) a) 2х-у -2%3D2 [3 0 -3 0 4x-2z-1 0 1 1 C= 3 A x+4y+z 4 2 1 0 2 -2 0 2 1 d) b-c+d 2 c) 2 -20 2 0 2a+3b-4c+d = -1 3 010 C A -2 a-2b+2c-d= 0 0-1 |-2 0 3 4 b-c 1 2. For each...
These are linear algebra problems. 1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
191 Problem 2. [30 marks] Consider the system in Problem 1 1. [5 marks] Determine its observability. 2. [15 marks] Design the observer with eigenvalues of-4+ j4. 3. [10 marks] Give the observer-based state feedback controller using the result in Problem 1. 191 Problem 2. [30 marks] Consider the system in Problem 1 1. [5 marks] Determine its observability. 2. [15 marks] Design the observer with eigenvalues of-4+ j4. 3. [10 marks] Give the observer-based state feedback controller using the...
Homework 1 Due day: February 6, 2019 Name: Score: Please give as complete answers as possible and show your work. 1.1 Determine whether matrix A is in the reduced echelon form and justify your answer: 4 3 6 3 0 1 28 A=10005 1.2 Determine the values of s such that the matrix below is the augmented matrix of a consistent system: 12 -7 19 -24 14 s 1.3 Solve the system of linear equations: rı + 212-13 =-1 1.4...
6F only please nas ne sam nection as - (+.-2,-1) (0) ns oppositely directed to v = (4,-2,-1) 6. Let u (-3,1.2), v (4. 0,-8), and w (6,-1. -4). Find the components of (a) v- (b) 6u + 2v (c) -vu (d) 5(v-4u) (e) -3( -8w) (f) ( 7. Lct u, v, and w be the vectors in Exercise 6 Find the comnanente oFthatr i (2u - 7w)-(8v u)