# 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.

View More On Wikipedia.org
1. ### 3x3 matrix with complex numbers

The attempt at a solution: I tried the normal method to find the determinant equal to 2j. I ended up with: 2j = -4yj -2xj -2j -x +y then I tried to see if I had to factorize with j so I didn't turn the j^2 into -1 and ended up with 2 different options: 1) 0= y(-4j-j^2) -x(2j-1) -2j 2)...
2. ### I Why are determinants in 2x2 matrices and 3x3 matrices computed the way they are?

Hi, I'd like to have a little insight about why the determinants of ℝ2x2 and ℝ3x3 matrices are computed that way. I know how to calculate said determinants in both the cases and I also know what's the meaning behind it thanks to "3blue1brown"'s youtube channel, which states that they are a...
3. ### Prove that If A,B are 3x3 tensors, then the matrix C=AB is also a tensor

I try to solve but i have 1 step in the solution that I don't understand who to solve. Below in the attach files you can see my solution, the step that I didn't make to prove Marked with a question mark. thanks for your helps (:
4. ### Find the rank of this 3x3 matrix

Hi, I was trying to find the rank of following matrix. I formed the following system and it seems like all three columns are linearly independent and hence the rank is 3. But the answer says the rank is '2'. Where am I going wrong? Thanks, in advance!
5. ### Find the eigenvalues of a 3x3 matrix

Hi, I have a 3 mass system. ##M \neq m## I found the forces and I get the following matrix. I have to find ##\omega_1 , \omega_2, \omega_3## I know I have to find the values of ##\omega## where det(A) = 0, but with a 3x3 matrix it is a nightmare. I can't find the values. I'm wondering if...
6. ### I Meaning of Third Eigenvalue in a Tilted Ellipse in a 3x3 Matrix

While reading the Strang textbook on tilted ellipses in the form of ax^2+2bxy +cy^2=1, I got to thinking about ellipses of the form ax^2 + 2bx + 2cxy + 2dy + ey^2=1 and wondered if I could model them through 3x3 symmetric matrices. I think I figured out something that worked for xT A x, where x...
7. ### LU Factorization on Ti-89: 3x3 & 4x4 Matrix Solutions

What's the correct command for finding an LU factorization of a 3x3 and 4x4 matrix on Ti-89 graphing calculator? I'm trying to find the correct answers and verify/check my answers for Linear Algebra problems.
8. ### A What Does the Book Say About the Eigenvalues of 3x3 Matrices?

I found in one book that every quadratic matrix 3x3 has at least one eigenvalue. I do not understand. Shouldn't be stated at least one real eigenvalue? Thanks for the answer.
9. ### Proof a property for a 3x3 matrix

Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.

11. ### Advice on calculating the determinant for 3x3 Matrix by inspection

Homework Statement The problem is to calculate the determinant of 3x3 Matrix by using elementary row operations. The matrix is: A = [1 0 1] [0 1 2] [1 1 0] Homework EquationsThe Attempt at a Solution By following the properties of determinants, I attempt to get a triangular matrix...
12. ### A Covariance matrix size: 3x3 or 4x4?

Hello, I follow the post https://www.physicsforums.com/threads/cross-correlations-what-size-to-select-for-the-matrix.967222/#post-6141227 . It talks about the constraints on cosmological parameters and forecast on futur Dark energy surveys with Fisher's matrix formalism. Below a capture of...
13. ### I Why can't I reach every cell in a 3x3 square?

Hi, I was playing this game in which you start from any cells of a 3x3 or 5x5 square and draw a line that loops through every cell in the box. The line can go only through a vertical or horizontal side (not diagonally). When you start from certain cells (problem cells), you can't reach at...
14. ### 3x3 Invertible transformations

Homework Statement \mathbb{P}^{2} is an affine plane of 2 dimensionsThe Attempt at a Solution Take for example the affine plane with z=1. Then I take a general vector v= [x,y,1] and i apply the transformation B and then the transformation A. So i get Bv=f(v) and Av=cf(v). To me this...
15. ### Calculating Eigenvectors for a 3x3 Matrix: Understanding the Process

Hi, I am trying to find the eigenvectors for the following 3x3 matrix and are having trouble with it. The matrix is (I have a ; since I can't have a space between each column. Sorry): [20 ; -10 ; 0] [-10 ; 30 ; 0] [0 ; 0 ; 40] I’ve already...
16. ### Hill Cipher- Potential Cribs for 3x3 Matrix

Homework Statement I've created code to crack a Hill Cipher (n=3). I'm unsure which cribs to try to crack a specific code. Would anyone mind posting ideas? The crib must be 9 letters in length. Homework EquationsThe Attempt at a Solution
17. M

### Constructing a 3x3 Linear system question

Homework Statement Construct a 3 × 3 example of a linear system that has 9 different coefficients on the left hand side but rows 2 and 3 become zero in elimination. If the right hand sude of your system is <b1,b2,b3> (Imagine this is a column vector) then how many solutions does your system...
18. ### I Rotation Matrix for Vector v=(a,b,c) by Angle θ | Efficient Computation Method

Hello! I need to find the rotation matrix around a given vector v=(a,b,c), by and angle ##\theta##. I can find an orthonormal basis of the plane perpendicular to v but how can I compute the matrix from this? I think I can do it by brute force, rewriting the orthonormal basis rotated by...
19. ### Determinant of a 3x3 matrix via row reduction

Homework Statement Show that the determinant of is (a-b)(b-c)(c-a) Homework Equations Row reduction, determinants The Attempt at a Solution Apparently I got a (a-b)^2 instead of (a-b) when I multiplied them up. It would be grateful if someone can point me out where the mistakes are.
20. ### Spatial Filtering 2d numpy array with a 3x3 mask

I have large 2d matrices from dicom files that i wish to filter with a 3x3 mask. the image arrays are of varying size and are padded with one border of zeros for the edge handling of the mask. i need to iterate over every element in the array and multiply it by the mask. I've done it in SciLab...
21. ### Prove 3x3 Skew symmetric matrix determinant is equal to zero

Homework Statement Hi there, I'm happy with the proof that any odd ordered matrix's determinant is equal to zero. However, I am failing to see how it can be done specifically for a 3x3 matrix using only row and column interchanging. Homework Equations I have attached the determinant as an...
22. ### I General form of symmetric 3x3 matrix with only 2 eigenvalues

I'm looking for the general form of a symmetric 3×3 matrix (or tensor) ##\textbf{A}## with only two different eigenvalues, i.e. of a matrix with the diagonalized form ##\textbf{D}=\begin{pmatrix}a& 0 & 0\\0 & b & 0\\0 & 0 & b\end{pmatrix} = \text{diag}(a,b,b)##. In general, such a matrix can be...
23. ### I How to Solve for a 3x3 Matrix Using A and B Vectors?

Hi all, I have this data that can be described by M*A = B, where M is a 3x3 matrix and A and B are 3x1 vectors. Since I know and can collect A and B data, and I have 9 unknowns in the 3x3 matrix, I thought that collecting 9 pairs of A and B vectors would yield the matrix M's coefficients via 9...
24. ### Solve 3x3 Matrix Equation: x, y, z Variables

Homework Statement Find a 3x3 matrix A that satisfies the following equation where x, y, and z can be any numbers. ## A \begin{vmatrix} x \\ y \\ z \end{vmatrix} = \begin{vmatrix} x + y \\ x - y \\ 0 \end{vmatrix}##Homework EquationsThe Attempt at a Solution I attempted to solve this like...
25. ### Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?

I have a doubt... Look this matrix equation: \begin{bmatrix} A\\ B \end{bmatrix} = \begin{bmatrix} +\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\ +\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} = \begin{bmatrix}...
26. ### 3x3 matrix inverse unit vector

Homework Statement Hi! I have the 3x3 matrix for L below, which I calculated. But now I need to figure out how the equation below actually means! Is it just the inverse of L (L^-1)? I cannot proceed if I don't know this step. Homework Equations See image The Attempt at a Solution I put in...
27. ### What subspace of 3x3 matrices is spanned by rank 1 matrices

So that's the question in the text. I having some issues I think with actually just comprehending what the question is asking me for. The texts answer is: all 3x3 matrices. My answer and reasoning is: the basis of the subspace of all rank 1 matrices is made up of the basis elements...
28. ### Determinant of 3x3 matrix equal to scalar triple product?

The determinant of a 3x3 matrix can be interpreted as the volume of a parallellepiped made up by the column vectors (well, could also be the row vectors but here I am using the columns), which is also the scalar triple product. I want to show that: ##det A \overset{!}{=} a_1 \cdot (a_2 \times...
29. ### Can quaternion group be represented by 3x3 matricies?

Hi, The Quaternion group, ##Q=\{1,-1,i,-i,j,-j,k,-k\}##, can be realized by ##2x2## matricies: ## \begin{align*} 1=\begin{bmatrix} 1,0 \\ 0,1\end{bmatrix} &\hspace{10pt} i=\begin{bmatrix} \omega,0 \\ 0,-\omega\end{bmatrix} & \hspace{10pt}j=\begin{bmatrix} 0,1 \\ -1,0\end{bmatrix} &...
30. ### 3x3 patch antenna trasmission line designing problems

Hello, I'm currently engaged on a project where I need to design a 3x3 rectangular patch antenna array operating 1.5~5.8GHz on FR4 h=1.6mm substrate. I've studied the single element design and some TL matching techniques like the quarter wavelength but I can't put together a 3x3 elements...
31. ### Find a 3x3 Matrix such that....

Homework Statement Find a non zero matrix(3x3) that does not have in its range. Make sure your matrix does as it should.The Attempt at a Solution [/B] I know a range is a set of output vectors, Can anyone help me clarify the question? I'm just not sure specifically what its asking of me, in...
32. ### MHB Eigenvector of 3x3 matrix with complex eigenvalues

Matrix A: 0 -6 10 -2 12 -20 -1 6 -10 I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of: 1 0 0 | 0 0 1 0 | 0 0 0 1 | 0 So, how do I find the nonzero eigenvectors of the...
33. ### Find all orthogonal 3x3 matrices of the form

Homework Statement Find all orthogonal 3x3 matrices of the form \begin{array}{cc} a & b & 0 \\ c & d & 1\\ e & f & 0 \\\end{array} Homework Equations There are many properties of an orthogonal matrix. The one I chose to use is: An n x n matrix is an orthogonal matrix IFF $$A^{T}A = I$$. That...
34. ### Solve 3x3 Numerical Puzzle: Can it Be Done?

1. In a 3 x 3 square, place the numbers 2,2,2,3,3,3,4,4,4 in it so that when any line of three numbers is added up in any direction (including diagonally) the total is always 9. 2. I have tried for hours, can anyone tell me if this problem is actually possible? The best I get is when I do 234...
35. ### Finding eigenvectors of 3x3 matrix

Hi, I have an issue with zeroing the 3x3 matrix to find the eigenvector. I have found the characteristic equation for the 3 eigenvalues. the matrix is 1 1/2 1/3 1/2 1/3 1/4 1/3 1/4 1/5 The equation i got is -A^3 + (23/15)A^2 - (127/720)A + (1/2160) which...
36. ### What is the inverse of the 3x3 matrix mod 26

Homework Statement What is the inverse of the 3x3 matrix mod 26? K = \begin{pmatrix} 17 & 17 & 5\\ 21 & 18 & 21\\ 2 & 2 & 19 \end{pmatrix} Homework Equations The Attempt at a Solution So I found all the cofactors and then took the transpose of the matrix. I then...
37. ### Finding the eigenvalues of a 3x3 matrix

Homework Statement A = 7 -5 0 -5 7 0 0 0 -6 Can you please show your method aswell. Every time I try I get the wrong answer. FYI Eigen values are 12.2,-6The Attempt at a Solution so far I got: det = 7-λ -5 0 -5 7-λ 0 0 0 -6-λ Im unsure what to do next. I tried doing...
38. ### Solving a 3x3 Matrix: Find the Answer

Homework Statement Given that |a b c| =-6 |d e f| |g h i| find |-3a -3b -3c | |d e f | |g-4d h-4e i-4f | Homework Equations NA The Attempt at a Solution I am not sure where to start to solve this question. I am familiar...
39. ### Determinant of 3x3 matrices: Is a matrix with all odd entries a multiple of 4?

I need to prove that a 3x3 matrix with all odd entries will have a determinant that is a multiple of 4. This is how I set it up: I let A = { {a, b, c}, {d, e, f}, {g, h, i} } with all odd entries then I define B = { {a, b, c}, {d + na, e + nb, f + nc}, {g + ma, h + bm, i + cm} } where I add...
40. ### MHB Geometric action of an arbitrary orthogonal 3x3 matrix with determinant -1

Hi, I have a question about describing geometrically the action of an arbitrary orthogonal 3x3 matrix with determinant -1. I would like to know if my proposed solutions are satisfactory, or if they lack justification. I have two alternate solutions, but have little confidence in their validity...
41. ### Pertubation theory for 3x3 matrix

Some one knows a study material to diagonalize a matrix mass for 3 neutral scalar using perturbation theory like M^2=\left(\begin{array}{ccc} 2 \lambda_{\phi} v_{\phi}^2 &\lambda_{\phi \sigma } v_{\phi}v_{\sigma} & \lambda_{\phi\eta} v_{\phi} v_{\eta} \\...
42. ### Equal flow distribution to 3x3 grid

This may be more of a math problem; it arose out of my curiosity of manipulating LED matrices and reminds me of a traffic flow problem, but I am sure it can model a variety of applications. Its not a homework problem but would probably make a good one! You have a 3x3 grid of points, each...
43. ### How many 3x3 matrices can you find

Homework Statement My instructor wants to know if there are finite or infinite amount of solutions Homework Equations Matrix Multiplication The Attempt at a Solution I pretty much turned A into a 3x3 matrix like this... | A11 A12 A13 | | A21 A22 A23 | | A31 A32 A33 | and...
44. ### 3x3 Diagonalizable Matrices over GF(2)

Does anyone know where I can find or how I can compute (without checking all 512) the 8 diagonalizable 3x3 matrices over GF(2)? GF(2) means the entries are 0's and 1's. I'm working on some graph polynomial research and to check out a formula I'm working with I would have to take a sum over these...
45. ### 3x3 Identity and rotation matrices and how they work

I'm trying to rotate a point about the origin (0,0,0) and starting with an identity matrix, this works fine for the x- and y-rotation axes, but fails with the z-axis, where the point just sits in place. \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} M_{ID} \times M_Z...
46. ### Time-Dependent Degenerate Pertubation Theory for 3x3 matrix

Homework Statement H0 = [2,0,0;0,2,0;0,0,4] H1 = [0,1,0;1,0,1;0,1,0] Find energy eigenvalues to 2nd order. Homework Equations The Attempt at a Solution I know that I need to diagonalize the perturbation in the 2x2 subspace (for my 2 degenerate eignevalues of 2 but I'm not sure...
47. ### Finding eigenvalues of a 3x3 matrix

Homework Statement Find the eigenvalues | 1 2 -1| | -5 7 -5 | | -9 8 -7| Homework Equations The Attempt at a Solution I know that i need to add a -λ to every term in the trace so my matrix becomes | 1-λ 2 -1| | -5 7-λ -5| | -9 8 -7-λ| Then i need to...
48. ### Determining if a 3x3 matrix is negative semidefinite

Homework Statement I have the matrix A = [-10 3.5 3; 3.5 -4 0.75; 3 0.75 -0.75] I need to determine whether this is negative semidefinite. Homework Equations The Attempt at a Solution 1st order principal minors: -10 -4 -0.75 2nd order principal minors: 2.75 -1.5...
49. ### Finding basis of 3x3 matrix space

Homework Statement For my homework assignment, I'm supposed to find a basis for the space of 3x3 matrices that have zero row sums and separately for zero row columns. I am having a hard time with this as it seems to me that there are a lot of combinations I have to consider. For the first...
50. ### Finding an eigenvector of 3x3 matrix

Hi, I'm trying to find an eigenvector of a matrix. I know that λ = 1, so my matrix (A - λI) is [-0.5253, 0.8593, -0.1906; -0.8612, -0.5018, 0.1010; 0.1817, 0.1161, -0.0236] And from rows 2 and 3 I get these simultaneous equations -0.8612t_{1}-0.5018t_{2}+0.1010t_{3}=0...