(14) (7 marks) Find a Jordan canonical form of the matrix 13 0 0 0 0...
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J under each of the following assumptions (i) A has only eigenvalue namely 4 and dim N(A- 41) = 4. one (ii) dim N(A 21) = 5. (ii dim N(A -I) = 3 and dim N (A 31) 2. (iv) det(A I) = (1 - )2(2 - A)2 (3 - ) and dim N(A - I) dim N(A - 21) 1 (v) A5 0 and...
using the technique pictured, find the controllable canonical form of In this section we shall first review technlqes into canonical forms. Then we shall review the invariance property of the Consider conditions for the controllability matrix and observability matrix orming State-Space Equations Into Canonical forms. crete-time state equation and output equation x(k +1) Gx(k) + Hu(k) y(k) Cx(k) + Du(k) We shall review techniques for transforming the state-s (6-30) (6-31) pace equations defined by Equations (6-30) and (6-31) into the...
2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt) 2. Matrix B is defined as, -31 B=10-2 0 0-2 a. Find the Jordan form of matrix B b. Find exp (Jt), where J is the Jordan form of matrix B c. Find exp (Bt)
I need it in the Jordan Canonical Form. The solution should look like: (8 points) Solve the system of differential equations x'(t) = [-2 0 1 2 -3 2 -37 1 -4 x(t), x(0) = The only eigenvalue of this matrix is -3, a triple root. You must explicitly find any matrix involved, with the exception of any matrix inverses (in the same way that the solutions were done in class). Also, your answer cannot involve the imaginary number i....
Linear Algebra Problem! Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
1. For each of the following linear operators T:V + V, find the Jordan canonical form together with a Find the Jordan canonical basis B for V. Feel free to use a Wolfram Alpha or whatever to calculate the characteristic polynomial, but you should complete the rest of the question without computer assistance (i.e., show your steps). (a) The map T : R4 → R4 given by T(v) = Av where -3 1 27 _ A=1 -2 1 -1 2||...
DIRlag J12, 2, 2, 2)), JJ,J), (4, , , 2, 2)))! 7. Describe the Jordan canonical form matrices that are not similar to any Jordan canonical form besides themselves. g () Sunce is n dimensional and T. isolinoor mon such that for all
1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0 -3 1 2 0-1 0 0 0 (d) 2 2 21-1 2 (e) 0-2-5-3 -2 0 6 85 4 0 -5 3-3 -2-3 4 1. Find the Jordan canonical forms of the following matrices 0 0 -1 (c) 7 6-3 (b) 2 3 2 1 0 4 0 1 -3 -10-8-6-4 0...
0 1 0 01 1-16 0 0 0 #7 (15 points) The canonical form of a matrix is 1000 21: 9. Write its eigenvalues below: LO 0 -2 01 Suppose only two eigenvectors are known, Vi= Suppose only two oiewentos ne koum, Vi-| .md v=. How will you find the othe 0. How will you find the other eigenvectors? Show the main steps and write the form of the solution, X=
Complex Jordan Form to Real Jordan Form. Below is the Jordan form for some matrix A. However, it is in complex form. What is the Real Jordan Form of this matrix? That is, a Jordan form with all entries being real values. ( -1) 1 Ο -1 Ο Ο Ο Ο Ο Ο Ο Ο 1 +Ι- Ο Ο 1-I-)