Recent content by ougoah

  1. O

    Diagonalizability of a matrix containing smaller diagonalizable matrices

    If an ##n\times n## matrix is diagonalisable, then it must have ##n## linearly independent eigenvectors. If you have a repeated eigenvalue with multiplicity ##k##, then the dimension of the corresponding eigenspace must also be ##k##. Is it possible you haven't found all the eigenvectors...
  2. O

    Diagonalizability of a matrix containing smaller diagonalizable matrices

    So you've shown that ##R## has ##n## linearly independent eigenvectors, since they come from different two matrices with no overlapping eigenvalues, and also where an eigenvalue does repeat within either ##A## or ##D##, the geometric multiplicity of the eigenvalue is equal to its algebraic...
  3. O

    Is the Function u(c, l) = 20000c + c^2 + l Quasiconcave?

    I don't think it is quasiconcave in the first quadrant. The level curves I get are parabolas, not circles, but in any case, the upper level sets in the first quadrant are shapes that curve around like a parabola and are not convex. Have you talked to your teacher again about this?
  4. O

    Hard integration by parts question,

    Think you forgot to put a square root in your question, or you wouldn't have got the answer you got. I used a sec substitution and got ##\displaystyle\ln\left(\frac{6+3\sqrt{3}}{4+\sqrt{7}}\right)##, which is slightly different to your answer.
  5. O

    Simple Linear Algebra matrix problem

    If the required answer is 7/2, it is wrong, as can be checked easily. What you described initially does work.
  6. O

    Oscillating bucket, variable mass

    Are you sure you can use the damping equation? The derivative of m(t) is a constant in this example, but m(t) is not. Isn't this required for the damping equation?
  7. O

    Why Does Kirchoff's Loop Rule Apply to AC Circuits Using Complex Numbers?

    I was wondering why Kirchoff's loop rule holds for the complex representations of voltage drops in AC circuits. That is, sum of complex voltage drops = 0. I tried working it out from Kirchoff's rule in DC, but am not sure how to proceed properly.
  8. O

    Proving Total Kinetic Energy of Particles

    I don't know why this was moved, since it is not a homework question; my textbook is missing this proof.
  9. O

    Proving Total Kinetic Energy of Particles

    For a system of particles, how would you prove that the total kinetic energy of the particles is equal to the kinetic energy associated with the center of mass motion plus the "internal energy"? (Where, I think, internal energy is the energy of the particles seen from the center of mass...