What is 3x3: Definition and 128 Discussions

3×3 is the second extended play by the English rock band Genesis, released in May 1982 on Charisma Records. Its three songs were originally written and recorded for their eleventh studio album Abacab (1981), but they were not included on the album's final track selection. 3×3 reached No. 10 on the UK Singles Chart. In the US, its tracks were included on the international edition of the band's live album Three Sides Live (1982). The lead track, "Paperlate", peaked at No. 32 on the US Billboard Hot 100 singles chart and No. 2 on the Billboard Mainstream Rock Tracks chart.

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  1. R

    Solving a 3x3 Matrix with Lambda: A Tutorial

    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...
  2. K

    Tips on finding the eigenvalues of a 3x3 matrix

    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 \[...
  3. P

    System of differential equations (classification of 3x3 case)

    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...
  4. E

    Onstruct a 3x3 matrix A that has eigenvalues

    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
  5. T

    Finding a Non-Diagonalizable 3x3 Matrix with 2 as its Only Eigenvalue

    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...
  6. J

    What is the general algorithm for computing the null space of a 3x3 matrix?

    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...
  7. J

    Diagonalizability of 3x3 Matrices with 3 Distinct Eigenvalues

    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
  8. K

    Solving 3x3 Magic Squares: 4/6-Folder Reflection & Found

    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...
  9. Saladsamurai

    How can I find the Eigenvector for a 3x3 matrix?

    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...
  10. T

    V is vector space of all antisimetric 3x3 matrices

    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|...
  11. S

    How do you find the determinant of a 3x3 matrix with polynomial equations?

    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...
  12. E

    General Form of 3x3 unitary matrix

    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...
  13. H

    Is a Real 3x3 Matrix with a Square of Identity Diagonalizable?

    [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...
  14. B

    How Do You Find Eigenvectors for a 3x3 Matrix with a Known Eigenvalue?

    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...
  15. C

    Solve 3x3 Matrix Determinant: a-1(-a-1-2a^2)+2a^3-10

    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...
  16. N

    How to determine if a 3x3 matrix is diagonalisable or not?

    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?
  17. G

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

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

    3x3 similar matrices defined by characteristic and minimal polynomials

    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)?
  19. R

    Finding a Basis for 3x3 Symmetric Matrices

    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...
  20. M

    Finding the determinant of a 3x3 matrix.

    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...
  21. E

    What is the smallest subspace of 3x3 matrices

    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...
  22. M

    How do you find the adjoint of a 3x3 matrix? can u explain example?

    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...
  23. M

    What Is the Correct Way to Calculate the Inverse of a 3x3 Matrix?

    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...
  24. S

    Understanding Determinants of a 3x3 Matrix: A Beginner's Guide

    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
  25. M

    Integrating a 3x3 orientation matrix

    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...
  26. SpaceTiger

    Diagonalizing a 3x3 second derivative matrix

    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...
  27. D

    Finding a 3x3 Matrix D that Satisfies a Given Equation

    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)...
  28. Y

    How to Calculate a 3x3 Rotation Matrix around a Given Axis?

    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?
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