determinant

  1. M

    Calculate a determinant

    How could i calculate determinant this matrix. if it doesn't have exact dimension
  2. M

    determinant of symmetric matrix of size (n+1)(n+1)

    Let for j = 0,. . . n aj = a0 + jd, where a0, d are fixed real numbers. Calculate the determinant of the matrix A of size (n + 1) × (n + 1)
  3. M

    Calculate the determinant of the matrix

    Let for j = 0,. . ., n aj = a0 + jd, where a0 and d are fixed real numbers. Calculate the determinant of the matrix A of size (n + 1) × (n + 1). Matrix A is below
  4. B

    Determinant of the conjugate matrix

    I'm proving that |detA|=1 if A is unitary matrix. I got to the point where det(A*)det(A)=1. I know that det(A*)=det(A) conjugated (because determinant is polynomial with real coefficients), but I don't know how to precisely say that. Is there a simple way to prove that?
  5. M

    Negative determinant is positive?

    Hello, I am looking at this question. "Determine a general form of the equation of the plane through each of the following sets of three points" P1(1,-2,3) P2(1,0,2) P3(-1,4,6) This seems simple enough. I get this matrix Figuring out the determinants for each will get me 12,-2,4 So...
  6. C

    Best way to calculate a 5x5 determinant?

    I have this 5×5 matrix A=\begin{bmatrix} 1 & 2 & 3 & 4 & 5\\ 4 & 3 & 4 & 0 & 0\\ 8 & 6 & 7 & 2 & 0\\ 12 & 9 & 10 & 3 & 0\\ 16 & 12 & 13 & 4 & 0 \end{bmatrix} and I inquire: What would be the "best" way to solve it? (faster, easier). From what I see in most examples on the internet, they...
  7. Z

    double integral with Jacobian determinant

    Suppose we want to integrate f(x, y) = x + y over the diamond U with boundary lines y = x + 1, y = x - 1, y = -x + 1 and y = -x - 1 Fill in the three blank spaces below (two bounds and the integrand) to write the integral of f(x, y) = x + y as an integral in u and v: Using substitution x =...
  8. S

    Determinant of 6*6 matrix

    I am looking for the determinant of the following matrix. $$ \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & 2 & 0 \\ 0 & 0 & 1 & 2 & 0 & 0 \\ 0 & 0 & 2 & 1 & 0 & 0 \\ 0 & 2 & 0 & 0 & 1 & 0 \\ 2 & 0 & 0 & 0 & 0 & 1 \\...
  9. A

    Prove this New Determinant Property (New High-Order numerical methods)

    I suspect this property does not appear in the math literature, so please kindly prove it: Given the square matrix $A$ with $k=n+1$ rows and columns:% \[ A=% \begin{pmatrix} x_{1} & x^{n/k} & x^{(n-1)/k} & x^{(n-2)/k} & x^{(n-3)/k} & \cdots & {x}^{3/k} & {x}^{2/k} & {x}^{1/k}\\ 0 &...
  10. S

    Determinant related question!

    So I have got this problem. I'd be happy if someone can solve it for me, i'm currently in a big rush and it's the only one that I've got left to complete my assignment My assignment is : Find real number t such that : The results should be : t1 = -1 and t2 = 0 I know I should...
  11. D

    How do I find the determinant of this matrix?

    I have the following matrix: A - square matrix of n*n as follows: I figured out that the determinant is (-1)^n(n-1), but how do I prove it?
  12. G

    Determinant of matrix with Aij = min(i, j)

    Given a n×n matrix whose (i,j)-th entry is i or j, whichever smaller, eg. [1, 1, 1, 1] [1, 2, 2, 2] [1, 2, 3, 3] [1, 2, 3, 4] The determinant of any such matrix is 1. How do I prove this? Tried induction but the assumption would only help me to compute the term for Ann mirror.
  13. H

    Kronecker product identity

    Hi, during my exploration of some matrix operations I came to a suspicion that following itentity holds (A,B are square matrices both with n rows and n columns and \otimes is so called Kronecker product): det(A\otimes B-B\otimes A)=0 Do you know a proof of this fact? (I have tried to use this...
  14. S

    sample size determinant

    Hi everyone, I'm trying to determine a sample size. I am listening to calls to a Contact Centre from customers with Internet Banking or a banking app. I'll be listening for 3 different areas. area 1 gets 3.3 million calls annually area 2 gets 1.3 million calls annually area 3 gets 800k...
  15. W

    Coefficient of bivariate polynomial as a determinant of matrix

    Given $$ \begin{bmatrix} a\\ b\\ c\\ d\\ \end{bmatrix}=\begin{bmatrix} a_0t^3+a_1st^2+a_2s^2t+a_3s^3\\ a_4t^2+a_5st+a_6s^2\\ a_7t+a_8s\\ a_9\\ \end{bmatrix} $$ the following equation holds: $$ -\frac{1}{d} \begin{vmatrix} d&c&b&a&0\\ 0&d&c&b&a\\ 3d&2c&b&0&0\\ 0&3d&2c&b&0\\ 0&0&3d&2c&b\\...
  16. W

    determinant n by n matrix

    A n by n matrix A is given by that the (kth row, lth collumn) entry =k+l. What is the determinant of this matrix? How to tackle this problem? I know how to do it for a specific n but how to do it leaving n as a variable for n= 3 I would get a matrix like below. (1+1) (1+2) (1+3) (2+1)...
  17. F

    Determinant of a matrix

    See this videos; Determinant of order 3: https://www.youtube.com/watch?v=J4axr4_Ddao Determinant of order 2: https://www.youtube.com/watch?v=5fwBUaKYYrQ Determinant of order 1: https://www.youtube.com/watch?v=Kl9gWbhGbD0
  18. I

    Calculate determinant

    Hello, When i used green ellipse for calculate determinant, i have difference answer till when i used red ellipse. Why ? :eek:
  19. A

    Need help (determinant with a parameter)

    hello all . I have Question about the determinant and linearly dependent and it's : Let : a) Find det(B) in terms of k; b) For what value(s) of k are the column vectors of B linearly dependent; c) For k = 0, find det(B) and . can some one help me in this question and...
  20. A

    Find determinant and linearly dependent

    hello all . I have Question about the determinant and linearly dependent and it's : Let : a) Find det(B) in terms of k; b) For what value(s) of k are the column vectors of B linearly dependent; c) For k = 0, find det(B) and . can some one help me in this question and...