3x3 Definition and 125 Threads

Homework Statement Given the matrix A= 1 -1 -1 -1 1 -1 -1 -1 1 Find the eigenvalues.Homework Equations I = identity matrix The Attempt at a Solution det(A-xI) = (1-x)3 - 2 - 3*(1-x) = 0 ⇔ ⇔(1-x)3 - 3*(1-x) - 2 = 0 I can't find a way to solve this equation... Any help...

Let's say you have a 3x3 matrix and it's invertible. Let's call it A If you were to find a basis for the nullspace of A, would the basis just be the original 3 column vectors of A?

any1 can please tell me the eigen vector for following matrix: [0 0 a 0 0 0 0 0 0] please elaborate ur answer!

Homework Statement Find the 3x3 matrix X such that XA=B, where 1 1 1 A= -1 0 -2 1 0 -1 1 3 0 B= -2 1 -2 1 4 -1 The attempt at a solution I understand how to do AX=B just fine, but XA=B is confusing me. I tried doing [x y z] A, but not sure if that's even...

I am wondering how one would find a the determinant of a 4x4 or greater. This isn't an urgent question, just a curiosity.

Homework Statement Find the eigenvalues of: |13 -30 0| |1 0 0| |0 1 0| Homework Equations Equation for the eigenvalues: det(A-λI)=0 Cofactor expansion = det A = a11(a22a33-a23a32)+a12(a23a31-a21a33)+a13(a21a32-a22a31) The Attempt at a Solution |13-λ -30...

Homework Statement Find the general solution to the system of differential equations. Homework Equations The Attempt at a Solution I uploaded the original equation and my work so see the attachment. I want to know how they got the vectors the got typically when I have done 2x2...

Hi all, I have a fundamental question about ( mechanical) stress tensor. Stress tensor a 3x3 tensor whose 9 entries looks "scalars" but in figures, the stress is illustrated by nine "vectors". Does it mean the stress tensors is in fact a 3x3x3 tensor of scalars whose nonzero entries are ignored?

Hi all, do you know where i can find the 3x3 matrix representation of SU(2)? Which means basically rotation matrices for particles of spin 1. Thanks!

Homework Statement 1. Homework Statement [/b] Enumerate all possible Jordan forms for 3 x 3 systems where all the eigen-values have negative real parts. Do not use specific values. Instead, use possibilities like λ1; λ2; λ3, each with multiplicity 1, or λ (multiplicity 3). Homework...

Homework Statement Think of the following matrix A = \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right) as a transformatiom of \mathbb{R}^3 onto itself. Describe A as a projection onto a plane followed by a shearing motion of the plane. 2...

Find a nonzero 3x3 matrix A such that Ax is perpendicular to [1,2,3] for all x in R3 A vector perpendicular to [1, 2, 3] could be, say, [-2, 1, 0]. But what would be a general approach to finding a solution that would satisfy all x? Thanks!

Homework Statement Show that: (x^2) (2x) (-2) (2x) (2-x^2) (2x) (2) (-2x) (-x^2) = (x^2 + 2)^3 Do not use direct evaluation.Homework Equations The Attempt at a Solution As direct evaluation is not permitted, I'm wondering which method should I use? Thank you

Homework Statement Let B := 2 1 5 0 2 3 0 0 2. [Hint: Write B as a diag-matrix plus a nilpotent matrix.] Then B^2005 = ? Homework Equations The Attempt at a Solution so i found the eigenvalue to be 2, with a multiplicity of 3. When plugging the eigenvalue back into B, the original matrix, I...

Homework Statement 1 1 1 | 2 0 5 2 | 12 0 -4 8 | 0 Answer: 100 | -3 010 | 2 001 | 1 Homework Equations The Attempt at a Solution How did they get the answer? I went over how to do 2x2 w/ someone but 3x3 seems different. Basically this is how I'm...

I am confused as to what that means? Is that a coordinate system with 3 y-values?

Homework Statement i = the 3x3 matrix below 2-λ 0 1 -1 4-λ -1 -1 2 0-λ Using remainder and factor theorem find the 3 values of λ. Homework Equations |i| = a1|b2c3-c2b3|-a2|a2c3-c2a3|+a3|a2b3-b2a3| |a|=ad-bc The Attempt at a Solution(2-λ) |(4-λ x...

Homework Statement 3 wires and unknown tensions: Tab, Tbc, Tbd Flowerpot being suspended in equilibrium Fx = .05Tab - 0.728Tbc - 0.728Tbd = 0 lbs Fy = -.05Tab + 0.485Tbc + 0.485Tbd = 20 lbs (weight of flower pot) Fz = 0Tab + 0.485Tbc - 0.485Tbd = 0 lbs Homework Equations...

Homework Statement Let V be the spcae of all 3x3 matrices with real entries. Is W, the set of all 3x3 lower triangular matrices, a subspace of V? Why or why not? Homework Equations The Attempt at a Solution I just think that all 3x3 lower triangular matrices are included in...

Homework Statement So the 3x3 matrix involved is [3 -1 -1:-4 6 4:-1 1 1], The eigenvalues are L=6 and L=2. Homework Equations (A-LI)e=0 The Attempt at a Solution I stuck the eigenvalues into the matrix and got (-1 1 1)(not sure if its right) for L=2 but when I use L=6 in I can't...

Ive been trying for 3 hours now and can't seem to find the eigenvalues, the long polynomials are getting me confused, the matrix is [2 2 1:1 3 1:1 2 2] So far i did [2-L 2 1:1 3-L 1:1 2 2-L] then I do the normal way to find the determinant but after that I get a horrible polynomial...

this is my working out: http://i.imgur.com/1hsQS.jpg i sort of figured out how to do this a few mins ago lol. it doesn't seem too hard. it's sort of like... multiplying the first number in the matrix A by it's position in the matrix (x1 * x1) which is basically the coordinates of the value...

Homework Statement Find the general solution of dX/dt = AX(t) with the initial condition X(0) = (a1,a2,a3), where A = [0 1 0, 0 0 1, -1 1 1]. (Here, a comma signifies the end of a row). Homework Equations The exponential of A is e^A = ∑A^k/k! from k = 0 to k = ∞. The solution of dX/dt...

[Solved] Calculate the determinant of a 3x3 matrix Homework Statement Use elementary row operations to calculate the determinant of this 3x3 matrix. 1-a 1 1 1 1-a 1 1 1 1-a Homework Equations I think that the problem wants me to reduce this to...

Homework Statement Find the eigenvalues and an orthonormal set of eigenvectors for this matrix: |1 1+i 0| |1-i 1 0| |0 0 2| Homework Equations Find the determinant of A - xI, where A is the matrix, I is the identity matrix, and x denotes eigenvalues Set the...

Homework Statement http://img220.imageshack.us/img220/8187/questiong.jpg NOTE: I's are the unknowns, R's and emfs are given Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://img4.imageshack.us/img4/2180/solutionv.jpg Using Junction, loop rule to come up...

Let X denote the set of real symmetrical 3X3 matrix. Then (X,R) forms a linear space. What will be a basis set for this linear space? I would appreciate if someone can help me with the question. My understanding is in R3 space there could be many 3X3 matrix that could be the basis set for...

I encountered a system: 3x+5y+7z = 9 7x+3y-z=-5 12x+13y+14z=15 And the solution was infinite solutions. However, when looking at each equation, the constants (including coefficients) increase/decrease by a constant amount. 3x+5y+7z = 9 (+2) 7x+3y-z=-5 (-4) 12x+13y+14z=15 (+1) And I made other...

Homework Statement Prove or disprove the title of this thread. Homework Equations AX=(lamda)X The Attempt at a Solution I don't know where to start

Homework Statement Prove or Disprove: a 3x3 matrix A can have 0 as a eigenvalue Homework Equations (xI-A)=0 The Attempt at a Solution I believe it's false just because I've never seen it. I have no idea how to prove it.

Homework Statement Is the set of invertible 3x3 matrices a subspace of 3x3 matrices? Homework Equations The Attempt at a Solution I think no - the 'neutral 0 element' is not in the subset since the 3x3 0 matrix is not in the subset. Am I right? The book says it's not a subspace...

I have a midterm tomorrow and I find I'm quite slow at finding the determinant of a 3x3 matrix. Basically I'll only need to find the determinant to find the characteristic polynomial (at least for this class) and my prof on the board does it so fast, I'm wondering if there's some trick I missed...

Use the trace and determinant to compute eigenvalues. I know how to do this with a 2x2 but not sure how to do it with a matrix of nxn where n>2. \begin{bmatrix} \frac{1}{2} & \frac{1}{3} & \frac{1}{5}\\ \frac{1}{4} & \frac{1}{3} & \frac{2}{5}\\ \frac{1}{4} & \frac{1}{3} & \frac{2}{5}...

Homework Statement A is a 3x3 matrix with distinct eigenvalues lambda(1), lambda(2), lambda(3) and corresponding eigenvectors u1,u2, u3. Suppose you already know that {u1, u2} is linearly independent. Prove that {u1, u2, u3} is linearly independent. Homework Equations ?? The...

I need to compute the 3 eigenvalues and 3 eigenvectors of a symmetric 3x3 matrix, namely a stress tensor, computationaly (in C++). More specific details http://en.wikipedia.org/wiki/Principal_stress#Principal_stresses_and_stress_invariants". Basically 2 questions: 1. I am running into trouble...

Homework Statement Determine the eigenvalues and eigenvectors of the matric, A: A=\left[\begin{array}{ccc}1 & 1 & 0\\ 1 & -2 & 0\\ 0 & 0 & 1\end{array} Homework Equations I think i understand what is going on. I have found the matrix equation to be...

Homework Statement I need to find the inverse of the following matrix: [(cos*sin) (-cos) (sin2)] [(cos2) (sin) (-cos*sin)] [(sin) 0 (cos)] Homework Equations gauss-jordan elimination The Attempt at a Solution I know that in general, gauss-jordan elimination can...

Which is stronger 3x3 .25 inch thick square tubing or 4x2 .125 inch thick square tubing? When positioned vertically about 40inches high (considering that when positioned vertically it is completely secured), and a 20 inch square tubing attached at different levels between the 40 inches (either...

How to reduce a 3 by 3 inertia tensor to a scalor value? Hi I have the following tensor and i need to reduce it to a scalor quantity: 3 by 3 matrix 4150470.48 , 317.64, -353.42 317.64, 2047101.07,-1407556.61 -353.42, -1407566.61, 2284136.55 Please its urgent and any help would be...

Homework Statement My question involves finding the determinant of a 4x4 matrix, which I know how to do. The matrix is 0 1 2 3 0 1 2 5 0 3 5 6 0 0 0 0 Since the matrix has zeros in every row and column, its determinant will equal 0. However, I got to thinking that...

Homework Statement If A is a 3 x 3 matrix a1+2a2-a3=0, then A must be singular. I have the answering being true but how do I prove it?

How do I take the cross product of Two 3x3 Matrices. For example what is cross product of: [-1 0 0] [0 1 0] [0 0 1] x [0 -1 0] [1 0 0] [0 0 1] thanks, Della

I need to erect a hoist beam with a 10' span using square tubing. Which is stronger, 3"x3" 1/4" wall or 4"x4" x 3/16"? Also, how much weight could I lift at the center?

Homework Statement The set of all nonsingular 3x3 matrices does not form a vector space over the real numbers under addition. Why? Homework Equations A vector space over F, under addition, is a nonempty set V such that A1 Addition is associative A2 Existence of 0 A3 Existence of negative A4...

Substitute each of the capital letters by a different digit from 0 to 9, such that each of the columns, each of the rows and each of the two main diagonals of this 3x3 square have the common sum LRK. It is known that L is nonzero and, each of the numbers in the nine cells contains non leading...

Homework Statement In the space of 2 by 2 matrices, find a basis for the subspace of matrices whose row sums and column sums are all equal. (Extra credit: Find five linearly independent 3 by 3 matrices with this property) The Attempt at a Solution The first one is ok. The matrix is...

Hello Im trying to find the eigenvalues and eigenvectors of 3x3 matricies, but when i take the determinant of the char. eqn (A - mI), I get a really horrible polynomial and i don't know how to minipulate it to find my three eigenvalues. Can someone please help.. Thanks

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...