3x3 Definition and 128 Threads

Homework Statement I am having trouble figuring out lambda for the 3x3, I have only done 2x2. My matrix: 4 1 4 1 7 1 4 1 4 The Attempt at a Solution I know that when I add lambda (L) in it looks like 4-L 1 4 1 7-L 1 4 1 4-L When I do a 2x2, I would just cross multiply as...

I find it rather tedious to calculate the eigenvalues of a 3x3 matrix. For example The \emph{characteristic polynomial} $\chi(\lambda)$ of the 3$3 \times 3$~matrix \[ \left( \begin{array}{ccc} 1 & -1 & -1 \\ -1 & 1 & -1 \\ -1 & -1 & 1 \end{array} \right)\] is given by the formula \[...

Hi, i am new here and this is my first problem to post. As you probably know eigenvalues are used to determine the stability of critical points of systems of first-order, autonomous differential equations. I know how the method works for 2x2 systems. For example if the eigenvalues of matrix...

2. Construct a 3x3 matrix A that has eigenvalues 1, 2, and 4 with the associated eigenvectors [1 1 2]T, [2 1 -2]T and [2 2 1]T, respectively. [Hint: use P-1AP = K, where K is the diagonal matrix] hlp me... pls guild me to the step reli no idea how to do it

Homework Statement Find a 3*3 matrix A which is not diagonalizable and such that 2 is the only eigenvalue of A Homework Equations The Attempt at a Solution since λ=2,and it is a 3*3 matrix i get the det(λI-A)=(λ-2)^3=0 then λ^3-6λ^2+12λ-8=0 now i use...

There are 2 issues I want to talk about in this post. (1) General algorithm for gauss-jordan elimination computation of null space (2) Closed form solution to 3x3 null space Following the example here, https://en.wikipedia.org/wiki/Kernel_(linear_algebra) I thought a general algorithm to...

Homework Statement quick question, if there is a 3x3 matrix which has exactly 3 distinct eigenvalues why must it be diagonalizable? Homework Equations The Attempt at a Solution

3x3 magic squares * updated http://en.wikipedia.org/wiki/Magic_square#Types_of_magic_squares_and_their_construction given a 3x3 block with 3 numbers inserted e.g. |2|_|_| |_|_|6| |_|3|_| How would I solve this magic square? Is there a pattern for this? The method in wikipedia...

X'=\left[\begin{array}{ccc}4 & 1 & 4\\ 1 & 7 & 1\\ 4 & 1 & 4\end{array}\right]X After evaluating the determinant I get from the characteristic equation \lambda=0 \lambda=\frac{15\pm \sqrt{119}*i}{2} Now here is where I am not sure where to go. I need to create an Eigenvector. I stared...

Homework Statement V is vector space of all antisimetric 3x3 matrices. Find the coordinates of the matrix A= \left| \begin{array}{ccc} \ 0 & 1 & -2 \\ -1 & 0 & -3 \\ 2 & 3 & 0 \end{array} \right|\] relative to the base E_1= \left|...

M= |3-2x^3_____-4+2x^2+4x^3______0| |-x^3________1+x^2+2x^3_______0| |-8-6x^2_____16+12x^2____-1-3x^2| find the determinant. * I put the underscores for spacing.The Attempt at a Solution I first tried finding det(A) as if it was a regular matrix of numbers, but that doesn't...

Hi, Does anyone know the general form of a 3x3 Unitary Matrix? I know for 2x2 it can be parametrized by 2 complex numbers. I remember once seeing a general form for the 3x3 in terms of 6, I think, complex numbers. Anyway, I'm having trouble finding that now...so if anyone could help me it...

[SOLVED] Diagonalizing a 3x3 matrix Homework Statement I want to show that a real 3x3 matrix, A, whose square is the identity is diagonalizable by a real matrix P and that A has (real) eigenvalues of modulus 1. Homework Equations None. The Attempt at a Solution Since any matrix...

Homework Statement Given Matrix B: [ 1 2 1] [-1 2 -1] [ 2 -2 3] and knowing that one of the Eigenvalues is 4, find one other value and its corresponding eigenvector Homework Equations Bx=Lx (The basic idea behind eigenvectors) det(B-LI)=0 The Attempt at a Solution Ive...

The question is as follows: Solve for a: |(a-1) ( 1) (0) | ....|(-10) (a+1) (a^2) | =0 ....|(2a) ( 2) (-1) | (Sorry that is my attempt at the determinant of a 3x3 matrix - the brackets are there to show which bit goes with which as they seem to group...

Can anyone tell me how can we determine if a 3x3 matrix is diagonalisable or not?It is not a homework problem...But I need to know this.Say I am given a 3x3 real matrix...And I want to see if it is diagonalizable or not without brute evaluation...Then how can I dio this?

How can i do the divergence of a matrix 3x3?

Why do you guys think that given two 3x3 matrices, they are similar if and only if their characteristic polynomial and minimal polynomial are equal (this reasonably fails for 4v4 matrices though)?

This is the problem that I am working on. Find a basis for the vector space of all 3x3 symetric matricies. Is this a good place to start 111 110 100 using that upper triangular then spliting it into the set. 100 010 001 000 000 000 000 000 000 100 010 000 000 000 000...

Hello, I just finished doing a question in which I had to find the values of x y and z from 3 linear equations using Cramer's rule. I used row augmentation for the x and y but then for z I couldn't see any way of using row augmentation. So I looked in my notes and saw an example using...

I want to confirm something: what is the smallest subspace of 3x3 matrices that contains all symmetric matrices and lower triangular matrices? - identity(*c)? because that is the only symmetric lower triangular i could think of... what is the largest subspce that is contained in both of...

Hello everyone, I think i don't understand the inverses because i don't understand how u find the adjoint of a nxn matrix. The book has this example and i have no idea how they got from A to A adj, makes no sense to me! Here is the picture...

Hello everyone, i have no idea why i can't grasp this simple concept... i have: A = 1 4 9 0 1 9 0 0 1 I have to find A^-1, A inverse. So I found the determinant along row 3, 1*det(B) = 1; B = 1 4 0 1 det(B) = (1)(1) - (4)(0) = 1; so i take 1/det * A now wouldn't that just...

could someone please explain simply how to get the determinate of a 3 * 3 matrix I'm relly stuck I've looked through my textbooks but it only has examples of how to do it useing a grapgics calculator thanks

Hi there, (I hope this post is in the right forum) I'm trying to integrate a 3x3 orientation matrix using a vector representing rotational velocity (in 3d) This is the formula I'm using: newOrientation = orientation + (dt)(~w)(orientation) where w is the vector rotational velocity...

I've been working on this problem lately where I've been looking at the second derivatives of 2D and 3D density fields. Now, the second derivatives of the field can be represented in a matrix, which can be thought of as an N-dimensional ellipse with the principal axes aligned along some angle...

Hello everyone the following problem has me completely stumped, I am to find a certain 3x3 matrix D that satisfies the following equation: ADA^{-1} = \left(\begin{array}{ccc}1&0&0\\1&0&0\\1&0&0\end{array}\right) where : A = \left(\begin{array}{ccc}1&2&3\\0&1&1\\0&2&1\end{array}\right)...

Hi, if i want to find a 3x3 matrix R which represents a rotation of Pi/6 around the axis of rotation v(vector)={1, 2, 3}. how can i find it?