matrices

  1. M

    Algebra Word Problem

    I really don't understand how to solve this problem, can you please help me out? It would be greatly appreciated :) A rock concert brought in $432,500 on the sale of 9,500 tickets. If the tickets sold for $35 and $55 each, how many of each type of ticket were sold? Solve this problem using...
  2. J

    using determinants to prove invertible matrices

    Could really use some help. I'm getting lost in all of the notation Let A∈Cn×n, let det(λIn−A)=λn+∑k=0n−1akλk denote the characteristic polynomial of A. Prove that if A is invertible, then A−1=−1a0[An−1+∑k=1n−1akAk−1]
  3. Z

    Change the order of matrices in a matrix product

    Hi, I want to solve the Helmholtz-equation via diagonalization, therefore I must have the following structure: D_1U+UD^T_2 - \sigma U = F, where U is the unknown matrix, D_1,\ D_2,\ F are known matrices, ^T stands for the transpose and \sigma is a known constant. In cylindrical coordinate...
  4. X

    Solving Linear System Using Matrices! Help

    I need help solving the following system using the Gauss-jordan method. w/out calculator. thank you!!! 2x-1y+2z=9 1x+3y+0=5 3x+0+1z=9
  5. K

    example of a basis for m by n matrices

    which I translate as "For m by n matrices with elements from the field F let E^(ij) denote the matrix whose only non-zero entry is a 1 in the ith row and jth column. Then {E^(ij): for i between 1 and m, j between 1 and n} is a basis for m by n matrices with elements from the field F." I...
  6. J

    A is invertible iff it can be written as as a product of elementary matrices

    A is invertible iff it can be written as as a product of elementary matrices 9just want to make sure this is an appropriate proof) Proof A^{-1} = E_k\cdot\cdot\cdotE_2E_1 \Rightarrow (A^{-1})^{-1} = (E_k\cdot\cdot\cdot E_2E_1)^{-1} \Rightarrow A = E_1^{-1}E_2^{-1}\cdot\cdot\cdot E_k^{-1}
  7. J

    Elementary Matrices

    Questions: Find elementary matrices such that $E_n\cdot\cdot\cdot E_2E_1A=I$ where $A=\left[\begin{array}{cc}-3&6\\4&5\end{array}\right]$ I know an elementary matrix is one that can be changed into the identity matrix in one operation. I keep going through and I end up making it get further...
  8. J

    Good site for Matrices

    I use this site to double check inverses, matrix multiplication and determinants. It also gives the solution if you need it. Online Matrix Calculator
  9. P

    Why are they called orthogonal and not orthonormal matrices?

    Consider $A = \begin{bmatrix} 3/5 & -4/5\\ 4/5 & 3/5 \end{bmatrix}$. Clearly it is orthogonal. But its columns (and rows) are not just orthogonal but orthonormal as well. Why wouldn't we call this matrix orthonormal, then? Yet: $B = \begin{bmatrix} 5 & 0\\ 0 & -2 \end{bmatrix}$ has...
  10. M

    need some help with matrices

    I have a 2 by 2 matrix ive figured out the A.B product, hopefully its right ;-; so ive got the answer 4 8 -8 10 now im just not sure how to figure out the inverse of A and how to solve A X + I = B thanks in advance.
  11. M

    Minimise difference between two matrices

    Hello, I have been told that I need to minimise the error between two matrices, like so. {A_1}x = {A_2}s Where A_1 and A_2 are convolution folding matrices. x represents the desired filter and s the actual filter. I need to minimise the error between x and s. So using Cholesky, I would do...
  12. Q

    Commutativity in the space of linear transformation on a 2D vector scape

    A variant of a problem from Halmos : If AB=C and BA=D then explain why (C-D)^2 is commutative with all 2x2 matrices if A and B are 2x2 matrices. This result does not hold for any other nxn matrices where n > 2. Explain why.
  13. G

    Encoding matrices

    Hi, I've got a question about 2x2 and 3x3 encoding matrices. Clearly, to receive whole numbers under matrix multiplication (encryption), you would need a matrix with the determinant of 1 or -1. However, what does it matter if you use a 2x2 or a 3x3 encoding matrix, as long as the determinant = 1...
  14. M

    Matrices Transformation

    I would very much appreciate help with the following question: (i) Prove that the dot product of any two vectors u,v ∈ Rn is uTv. (ii) Given a Matrix A and vectors u,v ∈ Rn so that Au . Av = u . v , prove that A is orthogonal (for part (ii)we can assume that (AB)^t= B^t A^t)
  15. M

    Matrices

    I cannot get my head around this question. I would very much appreciate any help please. If we are given invertible matrices A, B and P so that A = PB, we can say that A is ‘left equivalent to B’. Prove that ‘left equivalence’ is an ‘equivalence relation’.
  16. N

    Determinants and complex numbers

    Hey everyone, Do you know if there are any links between the property of matrix determinants and Complex numbers. - a complex number being z=x+yi, where x and y are real numbers and i is the imaginary number which represents sqrt(-1) - a matrix being a 2x2 representation of a...
  17. N

    Matrices and Complex Numbers

    Hey, So I'm studying the links between complex numbers and matrices at the moment, and have been using the matrix 0 1 -1 0 to express the complex number i, (which represents the square root of -1). I was wondering if there are any other ways to express i as a matrix?? Thankyou!! :)
  18. L

    Re: Linear Algebra-Transition Matrices

    how to post the problem? Please, guide me
  19. G

    Linear Algebra-Transition Matrices

    Hey guys, I'm after some help on this problem. Help would be much appreciated.
  20. A

    Showing that a set spans the subspace of symmetric matrices

    I'm not really sure how to show this. It's the part about symmetric matrices that throws me off. What I know: A symmetric matrix has the property that A = A^T. To show that the set spans, I could create a matrix and show that if there are leading ones in each row, without a pivot in the...