Determinant Definition and 494 Threads

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 I was using the method shown in the following video; to find the determinant for the following 4x4 matrix 1 -2 3 -4 5 6 -7 8 -9 -10 11 -12 -13 14 -15 16 The Attempt at a Solution I was therefore expanding this out by...

Homework Statement If A is a square symmetric matrix nxn. Show that the determinant of A is the product of its eigenvalues. Homework Equations The Attempt at a Solution From spectral decomp. A = QλQ' |A| = |QλQ'| = |QQ'λ| = |Q||Q'||λ| = |λ| = the product of its diagonals...

Hi all... I've read on wikipedia (facepalm) that the first derivative of a determinant is del(det(A))/del(A_ij) = det(A)*(inv(A))_j,i If we go to find the second derivative (applying power rule), we get: del^2(A) / (del(A)_pq) (del (A)_ij) = {del(det(A))/del(A_pq)}*(inv(A))_j,i...

T:V -> V is linear. V is finite vectorspace of dimension m^2. T(M) = AMB where M is an mXm matrix and A, B are two fixed mXm matrices. I want to find the trace and determinant of this transformation. In the case where B is the indentity, I can show that the trace is m*tr(A) and the...

Hi guys. So I got this assignment, where I have to create my own function, which can calculate the determinant of any n x n matrix. The general formula we've been given is (recursive formula): det(A) = Sum[n,i=1] (-1)^{1+i} * a_{1 i} * det(A_{1 i}) where n is the length of the matrix...

Homework Statement Prove that for any matrix A, the following relation is true: det(e^{A})=e^{tr(A)} The Attempt at a Solution PROOF: Let A be in Jordan Canonical form, then A=PDP^{-1} where D is the diagonal matrix whose entries are the eigenvalues of A. Then...

for dimension 2, the following relation between determinant and trace of a square matrix A is true: det A=((Tr A)2-Tr (A2))/2 for dimension 3 a similar identity can be found in http://en.wikipedia.org/wiki/Determinant Does anyone know the generalization to dimension 4 ? lukluk

This is the quantum part for solving wavefunctions of mulit-electron atoms that need to be approximated by the variation method. Specifically we are supposed to differentiate this equation using the quotient rule : E(c1,c2) = [(c1^2*H11 + 2c1c2H12 + c2^2*H22) / (c1^2*S11 + 2c1c2*S12 +...

Homework Statement I have to find a determinant for 1 2 3 ... n -1 0 3 ... n -1 -2 0 ... n ... -1 -2 -3 ... 0 but I have very little clue how to proceed, because the mathematics material that I was given is very vague about this. Any help would be greatly appreciated. Homework...

i have a problem that i need to find the determinant of a 5x5 matrix. i have no clue how to go about solving this problem 2, -9, 1, 8, 4 -10, -1, 2, 7, 0 0, 4, -6, 1, -8 6, -14, 11, 0, 3 5, 1, -3, 2, -1

To determine if a matrix is invertible or not, can we determine this by seeing if the determinant of the matrix is zero or non-zero ? If it's zero, then the matrix doesn't exist because the inverse of the determinant would be an infinite number ?

Homework Statement Let A be an n x n matrix and \alpha a scalar. Show that det(\alpha A) = \alpha^{n}det(A) Homework Equations det(A) = a_{11}A_{11} + a_{12}A_{12} + \cdots + a_{1n}A_{1n} where A_{ij} = (-1)^{i+j}det(M_{ij}) The Attempt at a Solution det(A) = a_{11}A_{11}...

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 Show that det(eA)=etr(A) for A\inCnxn Homework Equations The Attempt at a Solution I am sooo bad at proofs. And I am still trying to wrap my brain around the concept of matrix exponentials. Can someone please get me started ...

the definition of a determinant is not simple at the first sight however we still have extremely simple relation det(AB)=det(A)det(B) it seems that the grassmann algebra is the essence behind determinant, isn't it?

Hi, Is det(A*)=(det(A))*, and why? Here ()* means complex conjugate only, and A is a complex matrix. Thanks in advance

Hello matrices masters, If A and B are nxn square matrices, is there an identity for the determinant of the block matrix A -B B A ? Lots of thanks and praises.

The following matrix problem occurred to me. I figured out the answer and would like to pose the problem. It's easy but would be best for an undergrad math major. The question: Consider a square n by n matrix with entries 1, 2, ..., n squared. Find a way to arrange these entries so that the...

Hello, I want to calculate the conditioning of a matrix, therefore I use the cond() commando in Matlab. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. If I calculate the condition number of...

Hi, if vector b * matrix K = 0 (bK=o) what methods can one use to show that the determinant of K is therefore also zero, without using eigenvalues. I have a feeling I am over complicating this. Knd regards Emma

Is the determinant a linear operation? I mean can we say that: \mathbb{E}[\text{det}]=\text{det}[\mathbb{E}] where E is the expectation operator?

Let β={u1, u2, ... , un} be a subset of F^n containing n distinct vectors and let B be an nxn matrix in F having uj as column j. Prove that β is a basis for Fn if and only if det(B)≠0. For one direction of the proof I discussed this with a peer: Since β consists of n vectors, β is a...

Homework Statement So I'm working on this proof. Given an n x n (square) matrix, prove that it's determinant is equal to the product of it's singular values. Homework Equations We are given A = U*E*V as a singular value decomposition of A. The Attempt at a Solution I was thinking that...

If A\in\mathbb{C}^{N\times N} is some complex matrix, is there anything we could say about the determinant of the matrix \left(\begin{array}{cc} \textrm{Re}(A) & -\textrm{Im}(A) \\ \textrm{Im}(A) & \textrm{Re}(A) \\ \end{array}\right)\quad\in\mathbb{R}^{2N\times 2N} where...

Homework Statement Let U be a unitary matrix. Show that for all vectors x that |Ux| = |x|Homework Equations U^H=U^{-1} |Ux|=|U||x| The Attempt at a Solution U^HU=I |U^HU|=1 |U^T|^*|U|=1 (det(U))^2 = 1 so det(U) = +/- 1 But that doesn't solve the question

Hi, I know how to calculate matrices determinants but I never figured out why they're so useful in many problems, like in integral variable substitution in calculus or to find eigenvalues. I don't have an intuitive idea of what a determinant is... I doubt it appeared in algebra just by...

Homework Statement Find the area of the region in the plane 34x2+14xy+5y2<=4 The Attempt at a Solution I know for this question it is best to find a standard matrix transformation, A that transform a region with a known area formula to this region bounded by an equation. So I let the...

does the determinant of square matrix have a physical meaning??

Homework Statement Let A be a 3 x 3 matrix satisfying the equation A^{2}-3A-2I=0 where I is the 3x3 identity matrix. Find det(A) given the det(A-3)=2 The Attempt at a Solution Well can't find anything like this in my textbook, notes or google. I imagine its a pretty simple matrix...

Homework Statement How do I show that det(I+Adt)=1+tr(A)dt +... ? Please help me :) Homework Equations The Attempt at a Solution

Homework Statement Find the curl of the vector field \mathbf{F} = <xyz,0,-x^2 y> The Attempt at a Solution I am mostly just having problems with computing the determinant. I could just go with crossing the first row and first column. But i noticed that the intermediate step...

Thank you!

Hi, Suppose we have the following matrix: \begin{center}\begin{pmatrix}\mathbf{L}&\mathbf{A}^T\\\mathbf{A}&\mathbf{0}\end{pmatrix}\end{center} where L is n-by-n matrix, A is m-by-n matrix. How to find the determinant of this square matrix? Thanks in advance

Homework Statement Compute this determinant \begin{vmatrix} 1 & 1& x& 1\\ x& 1& 1 &1 \\ 1& 1 & 1 &x \\ 1& x & 1& 1 \end{vmatrix} The Attempt at a Solution I tried swapping rows and eventually I got -\begin{vmatrix} x & 1& 1& 1\\ 1& x& 1 &1 \\ 1& 1 & x &1 \\...

[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...

Question: Prove that is U is an orthogonal matrix, then the determinant of U is equal to 1 or -1. Hint consider the equation U^t = U^-1 and use the properties of the determinant. ------------------------------------------------------------------------------------------- So far I only...

the problem is in the image

Hi there, I want to derive the derivative of the det(A+O'XO) with respect to X, where A, O', O and X are all matrix. Any suggestions, Thanks Baska

Homework Statement Hi everyone. I'm just going over some questions for a midterm and came upon one that I don't seem to understand. The question is follows Assuming a determinant |a b c | |d e f | = 4 |g h i | Find the determinant if |3a 2b 4c| |d e f | = ? |g h i |...

Homework Statement A= 1 2 CF.A= 3 -2 ADJ.A= 3 -2 2 3 -2 1 -2 1 Next i need to find determinant of A so then i can do ADJ.A / determinant.A Homework Equations How do i work out the determinant, is there a specific way and...

Homework Statement Homework Equations complex conjugate of a+bi is a-bi The Attempt at a Solution I defined M = A+Bi, where A and B contain real number entries. So that means that \bar{}M = A-Bi. Past that point, I don't know what to do. How can I find the determinant of the...

Homework Statement Solve this determinant \begin{vmatrix} 2 & 5 & 4 & 1\\ 4& 7 & 6 &2 \\ 6& -2& -4 & 0\\ -6& 7& 7&0 \end{vmatrix} The Attempt at a Solution I decided to get rid of the 1 at the corner of the first row by doing a row operation of R1 -> R1 - (1/2)R2 \begin{vmatrix}...

Homework Statement I need help in proving that if B is the matrix that results when a single row or column of A is multiplied by a scalar k then det(B) = k*det(A). Homework Equations The Attempt at a Solution The only way I could think of is setting up a general n x n matrix...

Homework Statement Suppose that the 6x6 matrix A obeys A^4 = 2A. Find all possible values of det A. Homework Equations Det(AB)=(detA)(DetB) The Attempt at a Solution Well my first guess is to show that A is either invertible or not invertible thus making Det A either non zero or...

Hi! I'm a bit confused on how I would compute a Vandermonde Determinant to a matrix. Is there a set formula I need to memorize? Any help would be appreciated. Maybe even a reliable link that could give me a step by step procedure on how to compute this?

1) If det(AB) = 0, is det(A) or det(B) = 0? Give reasons for your answer. Q1) First, cannot both det(A) or det(B) be 0? If it can, is this statement false. In any case, how can I prove that this is true for all statement since I only know how to find an example to show this is true, which...

Homework Statement I think I've got everything down pat, I just need someone to check that I'm correct. 2 equations: y= kx2+3x-6 y=x2-2x+3k For what values of k do the 2 equations intersect: a) no times b) one time c) 2 times The Attempt at a Solution equate the...

in varying an action like Polyakov's action with respect to the metric on the world sheet we have to consider the variation of the square root of the determinant. I have not found how to express the variation of the determinant of the metric. From reverse engineering I found that \delta(h)=2...

is multiplication of determinant commutative ? if so , then is this correct: |A||B|=|B||A|=|AB|=|BA| ? then what does |AB|=|BA| imply ??