# jordan

1. ### Gauss Jordan Elimination (2 problems)

Solve using Gauss Jordan Elimination Problem 1: 2x1+8x2-19x3=27 4x1+342-78x3=140 X1+7x2-16x3=28 Problem 2: 3x1-7x2-5x3=36 X1-4x2 _______ =17
2. ### Jordan measurable set

http://www.tau.ac.il/~tsirel/Courses/Analysis3/lect6.pdf Hi, i need help with the solution of problem 6h3 (c),on page 87. in the attached link. for p not smaller than 1,i think i know,but there must be a nice and compact solution. Thanks in advance.
3. ### Jordan Normal Forms

I am trying to revise for a test and i cannot get this question. And i have know idea where to start. Question Find the JNF for the matrix of the linear transformation T: P2 --> P2 given by T(p(x)) = p(x+1) Thankss any help is appreciated. I not great at JNF
4. ### volume of linear transformations of Jordan domain

Let T:\mathbb{R}^n\rightarrow\mathbb{R}^n be a linear transformation and R\in \mathbb{R}^n be a rectangle. Prove: (1) Let e_1,...,e_n be the standard basis vectors of \mathbb{R}^n (i.e. the columns of the identity matrix). A permutation matrix A is a matrix whose columns are e_{\pi(i)}...
5. ### Easy Gauss Jordan Elimination Matrix Problem

2x + 2y - z = 2 x - 3y + z = 0 3x + 4y - z = 1 Matrix form 2 2 -1 | 2 1 -3 1 | 0 3 4 -1 | 1 Could anyone sort of give me the steps to solve this? I'm having some trouble on it and I"m reviewing for an exam tomorrow. What sort of techniques should I be following? I normally just try to...
6. ### trace, jordan carnonical form

Can anyone help me showing that a)Let A is a realnumber matrix nxn. Show that tr (A) =sum of all eigenvalues of A. b)Let A is a realnumber matrix nxn. Show that det (exp (A)) = det (exp (J)) where J is the Jordan canonical form of A.
7. ### Jordan Form

Hi ALL !!! I must find the Jordan form of this operator: A(x_1, \ldots, x_6) = (2x_1+x_4+x_6,2x_2+x_5,2x_3,-x_1+3x_4+x_5+x_6,x_1+x_5-x_6,-x_1+x_4+x_5+4x_6) I found this matrix (is correct ?): \begin{pmatrix} 2 & 0 & 0 & 1 & 0 & 1 \\ 0 & 2 & 0 & 0 & 1 & 0 \\ 0 & 0 & 2 & 0 & 0 & 0 \\ -1 & 0 &...
8. ### jordan in power n

A is similar to G=diag(J_{2}(-1),J_{2}(1)) find the jordan form of A^{n} i have the formula that A^{n} similar to G^{n}=diag(J_{2}^{n}(-1),J_{2}^{n}(1)) so J_{2}^{n}(\lambda)=\left(\begin{array}{cc}\lambda^{n} & n\lambda^{n-1}\\ 0 & \lambda^{n}\end{array}\right) but in the book its...
9. ### jordan form question

does A=\left(\begin{array}{cc}a & 1\\0 & a\end{array}\right) and C=\left(\begin{array}{cc}a & b\\ 0 & a\end{array}\right) are similar? i know a law that if they have the same jordan form then they are similar i was told that if b=0 they the dont have the same jordan form if b=0 jordan form of...
10. ### non diagonisble jordan form

why if A is not diaginizable than there is a basis for which A coulnd be represented as block matrices ?
11. ### jordan basis problem

find th jordan form of A and find P for which J=P^{-1}AP A=\left(\begin{array}{ccc}1 & -3 & 3\\-2 & -6 & 13\\-1 & -4 & 8\end{array}\right) |kI-A|=\left|\begin{array}{ccc}k-1 & +3 & -3\\2 & k+6 & -13\\+1 & +4 & k-8\end{array}\right|=(k-1)[(k+6)(k-8)+52]-3[2(k-8)+13]-3[8-k-6]...
12. ### jordan block question

what is the difference between the jordan form of matrices A and diagonal block matrices similar to A ?
13. ### jordan forms

Hey, I am having some trouble doing these jordan form questions. 1. What are all the possible Jordan forms for a matrix whose characteristic polynomial is (\lambda+2)^2(\lambda-5)^3. 2. same as Q1 but the space of eigenvectors with eigenvalue 2 is 1-dimensional and is 2-dimensional for...
14. ### jordan form question

2)A) find the definative polinomial and the minimal polinomial of A=\left(\begin{array}{ccc}3 & 1 & -1\\2 & 2 & 0\\1 & -1 & 3\end{array}\right) find the primary decomposition of R^{3} in this case,and write the diagonal block matrices similar to A ? B) find the jordan form of A defined in part...
15. ### gauss vs gauss jordan

Hi Guys, I have a simple and basic question.... I know what Gauss elimination is, and what we use it for, and also knows what Gauss Jordan is...what I wanted to know, is when do I use each one ? I mean, in order to solve a system of equations, Gauss is enough, so why do I need Gauss Jordan...
16. ### Using Gauss Jordan Elimination for a problem

The problem reads: Three people play a game in which there are always two winners and one loser. They have the understanding that the loser gives each winner an amoutn equal to what the winner already has. After threegames, each has lost just once and each has \$24. With how much money did...
17. ### Jordan blocks

Dear MHF members, my problem reads as follows. I have some ideas about some parts of the problem but I would like to share it completely because I find the problem nice. Problem. Consider the system \mathbf{X}^{\prime}=\mathbf{A}\mathbf{X}, where \mathbf{A} is a 30\times30 constant matrix with...
18. ### Derivation and Jordan derivation

Let R be ring, and d:R\toR is aditif mapping then d is called derivation if d(ab)=d(a)b+ad(b) \forall a,b\in R d is called Jordan derivation if d(a^2)=d(a)a+ad(a)\forall a\in R Obviously any derivation is Jordan derivation. But the converse is not true. (is there any example to show this...
19. ### Linear algebra: Jordan forms & eigenvectors

Dear MHF members, I have the following problem. If the Jordan form of A is a single Jordan block of size n \times n, then how many independent eigenvectors does A have and what is the dimension of \ker (A-\lambda I)^2? Thanks for your help. bkarpuz
20. ### Jordan Normal Form Question

So far I've found the characteristic equation. [Math] (t-1)^2(t+2) [/tex] So the eigenvalues, are 1,1,-2 And I know the jordan matrix is along these lines(below) J= \begin{bmatrix}1&0&0\\0&1&0\\0&0&-2\end{bmatrix} But I literally have NO clue on where the extra 1's should be...