Determinant Definition and 494 Threads

Can anyone help with finding the determinant of vandermonde matrix or the way in which I can start the problem. I did with 4X4 matrix but I would have to show that the generalisation that I get works for nXn matrix. Please anyone

Do determinants of a 2-space matrix have a unit of [units]^2? Also, does A_[SIZE="1"]parallelogram = || u x v|| have a unit of [units]^2 too? This has confused me as Area has a unit of [units]^ 2 but the examples from the Contemporary Linear Algebra (Anton and Busby) textbook does not state...

I am having some trouble with the following linear algebra problems, can someone please help me? 1) Explain what can be said about det A (determinant of A) if: A^2 + I = 0, A is n x n My attempt: A^2 = -I (det A)^2 = (-1)^n If n is be even, then det A = 1 or -1 But what happens when n...

I am trying to find definition of determinant where the matrix entries may not be commutative, for instance quaternions or Clifford algebras. Does the minor expansion of determinant over a field still work over a non-commutative algebra?

Problem statement: Find the determinant of the following matrix by row reduction to echelon form. |1 3 3 -4 | |0 1 2 -5 | |2 5 4 -3 | |-3 -7 -5 2 | I reduced this matrix to |1 3 3 -4 | |0 1 2 -5 | |0 -1 -2 5 | |0 2 4...

Homework Statement Prove that (a b c d) is a unit in the ring M(R) if and only if ad-bc !=0. In this case, verify that its inverse is (d/t -b/t -c/t a/t) where t= ad-bc. Homework Equations An element a in a ring R with identity is called...

Homework Statement show that det(A)=(detA)*= det(A$) where * denotes complex conjugate and $ means transpose Homework Equations The Attempt at a Solution Please help me to start the problem.I am not getting a way.

Homework Statement Given the following 101x101 matrix: Akl where k and l are the row and column. Now Akl = (akl)=k^2+1 if k=l and (akl)=2*k*l else. I have to calculate the determinant of this matrix but have no clue how to start working, well I've some idea but it doesn't really help...

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...

Bonsoir everyone can anyone confirm if i got the answer right or wrong: Question: find the determinant of A. A is a matrix and is equal to 1 5 -3 3 -3 3 2 13 -7 (i think you've already guessed that i don't have latex) My answer: i got -18 I would be...

--- Find the determinant of a 5 X 5 matrix --- Homework Statement Find the determinant of the matrix. A = \left[\begin{array}{ccccc} 1 & 2 & 3 & 4 & 5 \\ 3 & 0 & 4 & 5 & 6 \\ 2 & 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 6 & 5 \\ 0 & 0 & 0 & 5 & 6 \end{array}\right] Homework Equations...

I have just tried to solve this problem and just wondering if I am right! 1) Compute the determinant of the matrix A -1 -1 1 x^2 y^2 z^2 0 -1 0 and find all real numbers x,y, and z such that A is not invertible. Okay so I found that the det=-z^2-x^2 So when the...

Use row and/or column operations to simplify the determinant of the following matrix A, by reduction to upper triangular form, then evaluate. A = \left(\begin{array}{cccc} 2 & 3 & 4 & 5\\ 0 & -1 & 2 & 1\\ 0 & 0 & 2 & 4\\ 0 & 3 & -6 & 0 \end{array} \right) Is there an simpler way to...

If A =\left(\begin{array}{ccc} 1 & 2 & 3 \\ -1 & 2 & 1 \\ 4 & 1 & -1 \\ \end{array}\right) and we want to zero the entries in the second row of A (i.e. make it 0 0 1 ). How do we get A =\left(\begin{array}{ccc} 4 & -4 & 3 \\ 0 & 0 & 1 \\ 3 & 3 &...

My lack of any shred of idea about the concept of the determinant is really beginning to bug me. Especially now that I have begun my Linear Algebra class. Is there anybody available to help explain (or link me to a good explanation) to me the idea behind it and what the value actually stands...

Show that evaluating the determinant of an n*n matrix by cofactors involves (n!-1) additions and \sum^{n-1}_{k=1}n!/k!multiplications. What does it mean? how to do it? Help!

Evaluate the following determinant. Write your answer as a polynomial in x. \begin{array}{|lcr|}a-x&b&c\\1&-x&0\\0&1&-x\end{array} Please help me! thanks.

If we let latin alphabets {i,j,k,...} denote the spatial indices, and the greek ones run from 0 to 3, then I've seen the following det| g_{\mu \nu} | = g_{00} det | g_{ij} | both in Landau's "Classical theory of fields", as well as ADM's paper on the initial value formulation of GR...

Let B \in \mathbb{R}^{n\times n}. Show that \det e^B = e^{tr B} where tr B is the trace of of B. Clearly e^{tr B} is the product of the diagonal entries of e^{B}. By the Jordan canonical for theorem, \exists P,J \in \mathbb{C}^{n \times n} where P is invertible and J is a diagonal sum of...

Hi, I'm curious if the following statement is true for all prime numbers n, \det_{\mathbb{Z}_n}M = (\det_{\mathbb{R}}M)\mod n where \det_F M is the determinant of M over the field F. Thanks. James

Hi guys, what doe it mean when we are asked to compute the determinant the following way: compute determinant across first row, down second column: |1_0_3| |2_2_1| |4_0_3| I know how to compute but here I need to understand the way to do it. Thank you B

The instructions for the section say: use the method of elimination to evaluate the determinants in problems 13-20. They are all 3x3 or 4x4 matrices I can't find an example of this in the book. Can someone outline the procedure for me? I've already solved these same problems using...

Let h = det h_{alpha beta}. The number of dimensions is not necessarily four. Show that \[ \delta h = -h h_{\alpha \beta} \delta h^{\alpha \beta} \, ; \] delta h is the variation in h. Not sure how to start.

Hello everyone I'm stuck on this problem, how its wrong, i got parts a and c, but b i can't get. Hre is what it says: Consider the following general matrix equation: [a1 a2] = |m11 m12| * [x1 x2] |m21 m22| which can also be written as A = MX Determinant of M = m11m22 - m12m21 A...

Hello everyone, I would rather find the cofactors and find the determinant than row reducing this, but is it possible, its not square! But our teacher is acting like its possible, so it must be! here is the equations: x+y+z = 4 2x-y+4z=9 3y-z = 1 so i got: 1 1 1 4 2 -1 4 9 0 3 -z 1...

Determinant problem, matrices! wee! Hello everyone... I got part a, and b, and I'm stuck on c... Suppose that a 4 x 4 matrix A with rows v_1, v_2, v_3, and v_4 has determinant det A = -6. Find the following determinants determinants: det[v_1 v_2 v_3 v_4 + 7*v_2]^T = ? I made it...

I'm confused, this question had 5 parts and i got the other 4 but this one I keep missing... If A is a 2x2 matrix... Det(A) = -5; The Det(-3A); The book said, if u multiply a column by a constant k then the determinant is also multiplied by k. So wouldn't the answer just be (-5)(-3) = 15...

why people need to define "determinant"? why people need to define "determinant"? Of course there are many reasons but what i want to know is the first one. -i.e- the origin of determinant

I have a matrix 4x4: 1,2,3,4 2,6,6,6 0,0,1,13 0,0,0,1 I need to find determinant. I am getting det=6. When I use online matrix calculator it gives me det=2. I tried reduce second row (2 row - 1(1 row)) and I got det=2 I'm confused. Why calculator gives me different answer?

What exactly is the relationship between the trace/determinant of two matrices with regards to similarity. I always thought that if the trace was the same, then there is a possibility that the matrices are similar and if the determinant was the same, then the matrices are similar. On a recent...

help me guys...

4x4 determinant(from my exam) a+b-- a--- a--- a a--- a+b-- a--- a a---- a-- a+b-- a detA=0 a---- a--- a--- a+b How do I find a and b?

Hi all, I don't understand one thing about linearity of determinants. In the book I have: \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{[i]} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j]} \end{array} \right) = \det \left( \begin{array}{ccc} . & . & . \\ . & . &...

Hello all. I'm stuck with this excercise that is asking me to proof that the determinant of the nxn matrix with a's on the diagonal and everywhere else 1's equals to: |A| = (a + n - 1).(a-1)^(n-1) So the matrix should look something like: [a 1 1.. 1] [1 a 1.. 1] [: ... :] [1 ..1 1...

What's the best way to take the determinant of a 3 X 3 matrix. It's actually a matrix in the form: \mathbf{A} - \lambda\mathbf{I} So I figured Gaussian elimination would be ugly, because of all the lambdas floating around. I tried the method of expansion by cofactors...and ended up with...

Proof, that determinant (with n rows and columns) | cosx 1 0 0 ... 0 0 | | 1 2cosx 1 0 ... 0 0 | | 0 1 2cosx 1 ... 0 0 | | 0 0 1 2cosx ... 0 0 | = cos nx |...... | |...

I've been doing revisions for my final exams, and I got stuck on the proof det A = det A^T, determinant of A = determinant of A transpose. How do I proof it?

I was doing a math project, and I was wondering if anyone knew how to solve a 4x4 determinant.

I won't to learn the logic behind a determinant, the math isn’t so hard you do that then you do that, you don’t need to think. But if I gone solve dynamic problems, then I must understand how a determinate work. Why do I get the information I want when I take the determinant? Do anyone got...

Ethn Dis. 2004 Summer;14(3):389-98. Race/ethnic and sex differentials in body mass among us adults.[/size] Denney JT, Krueger PM, Rogers RG, Boardman JD. Population Program, Institute of Behavioral Science, and Department of Sociology, University of Colorado, Boulder, Colorado...

J Nutr. 2004 Jul;134(7):http://www.nutrition.org/cgi/content/abstract/134/7/1786. Ethnicity and race influence the folate status response to controlled folate intakes in young women.[/size] Perry CA, Renna SA, Khitun E, Ortiz M, Moriarty DJ, Caudill MA. Department of Human Nutrition...

Is one way of looking of the determinant is its the area of the parallelogram formed by the vectors in 2 dimensions, the volume of the parallelpided in 3 dimensions etc. The sign of the determinant tells you something about the relative position of the vectors. This would make the...

Hi I'm new here and I hope that you will be able to give me a lot of help. My english is far to be perfect but sufficiant to asks you a lot of questions... (i hope so :wink:). First question : I'm looking for a complete proof (with all steps) of : \partial _h g = gg_{ij} \partial _h...

I seem to be still having problems with solving the determinant of a 4x4 matrix correctly. There are two methods I can use: Factor/Cofactor and reduction to triangular form. Ex: [ 1 2 3 4 -5 2 1 0 6 4 3 2 1 1 1 1] determinant is 2 based on the calculator Factor/Cofactor: I...