Determinants Definition and 169 Threads

A=[3 2 4 3 ;2 -1 2 -2 ; 1 2 0 -2 ;-2 -5 -5 -4] can smby pls show me how to perform this determinants pls thanx

hi, i seem to have some trouble proving: Suppose M = [A B:O C], where A is a kxk matrix, C is a pxp matrix, and O is a zero matrix. Show that det(M) = det(A)det(C). my attempt at a proof: det(M) = det(A)det(C) det[A B:O C] = det(A)det(C) AC - OB = det(A)det(C) AC =...

When making a slater determinant do you have to represent every electron in the atom, or just the electrons in the highest level?

I know what a determinant is and how to solve for it, but in the case of this n x n matrix on my homework, I'm at a complete loss as to how to even begin starting this. I don't expect anyone to work it out for me, just to give me a solid method for how to solve it and prove my method for the n...

Just wondering, how would you solve a problem such as this one: Suppose A is an 5 x 5 matrix, with det(A) = 2 find the following: det(A^-1 + adj(A)) Thanks in advance.

Okay, I need to prove that det(A^t) = det(A). I can see that it's true because I know columns and rows are interchangable (meaning you can use columns or rows when taking determinants), but I don't know how to prove this fact. Any help would be very appreciated.

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

Can anyone help me start this out? I got absolutely no clue. Q: If A and B are n x n matrices, AB = -BA, and n is odd, show that either A or B has no inverse. I know that we have to show that either det A is 0 or det B is 0, but I have no clue how to show it with the given information...

Can someone help me prove two theorems? I know they both are true, but can't come up with proofs. 1) Prove that a 3x3 matrix A is orientation preserving iff det(A)>0. 2) Prove that for A, B (both 3x3 matrices) that det(AB)=detA*detB. (A, B may or may not be invertible). THANK YOU!

without using any expansion method, prove the equality using the theorems in determinants...

How do computers evaluate determinants of large matrices? The cofactor method seems like it would be too time consuming. Does anyone know?

Prove that, if AA^T = A^TA = I_n, then \det{A} = \pm 1. This is daunting.

i'm reading and doing some work in introduction to linear algebra fifth edition, and i came across some problems that i had no clue. 1. An (n x n) matrix A is a skew symmetric (A(transposed) = -A). Argue that an (n x n) skew-symmetrix matrix is singular when n is an odd integer. 2. Prove...

I know how to find the determinant in general but these two problems here are tough for me: 1. Find the determinant of: 3 -1 0 0 0 -1 3 -1 0 0 0 -1 3 -1 0 0 0 -1 3 -1 0 0 0 -1 3 2. Find the determinant of: 0 2 2 2 2 2 0 2 2 2 2 2 0 2 2 2 2 2 0 2 2 2 2 2 0 Now, I know that I...

Hi, I' not sure if I've done this question correctly so I just want someone to tell me where I've gone wrong (if I have). Evaluate the following determinant as a product of two terms. Hence find, in terms of p the values of x for which it vanishes. Grr, I can't seem to use LaTeX properly...

:cry: :cry: :cry: Nobody wants to help me in the Software foum so I'm hoping someone loves me enough here to gimme some help! :shy: Basically, I need a Visual Basic program that can work out 4x4 determinants. I need it for a project and practical usage as well. Anyway - the...

hey, :eek: I want to use Visual Basic to create a programme that finds the determinant of a 4 x 4 matrix. I have some code and an idea how to do it but the process doesn't use arrays and is bloody long and doesn't work perfectly. My problem with the arrays is that I can't seem to get...

This is the first time I'm posting (or rather asking) anything here. I'm a student of elementary linear algebra, therefore please excuse me if my questions come across as dumb or if I make any mistakes: I have a question about determinants and whether or not a solution exists, etc. I will be...

I want to learn about determinants, but I'm just getting so bored studying the hundred and one ways to manipulate the determinant to find its value especially when they don't seem to have much value. What are determinants useful for?