Recent content by mivanova

  1. M

    Graduate Can you find the least-squares solution and projection of this matrix equation?

    I really need your help with this. Let A = (1 -2 -1 2 0 3 2 5) and b = ( 3 1 -4 2) (a) Find a least-squares solution of Ax = b. (b) Find the orthogonal projection of b onto the column space of A. (c) Compute the least-squares error ( in the solution of part ( a )). Thank you!
  2. M

    Show Linear Independence of Set with T:V->V Operator

    Can you help me with this, or at least give me an idea how to proceed: Let T:V->V be a linear operator on the vector space over the field F. Let v is in V and let m be a positive integer for which v is not equal to 0, T(v) is not equal to 0, ...,T^(m-1)(v) is not equal to 0, but T^m(v) is equal...
  3. M

    Graduate Suppose T is a linear map and dim(Im(T))=k

    Please, help me! Suppose T is a linear map and dim(Im(T))=k. Prove that T has at most k+1 distinct eigenvalues. Thank you in advance!
  4. M

    Undergrad Linear Transformations: Find Eigenvalues & Eigenvectors

    Please, help me! Suppose n is a positive integer and T is in F^n is defined by T(z_1, z_2, ... , z_n) = (z_1+ ... +z_n, z_1+ ... +z_n, ...,z_1+ ... +z_n) Determine all eigenvalues and eigenvectors of T. Thank you in advance!
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    Graduate Solving U, V, W Subspaces Problem

    Hi, It's indeed (direct sum) and I think that the statement is it's not true. I can't prove it though. Thanks!
  6. M

    Graduate Solving U, V, W Subspaces Problem

    Hi, I have thius problem to solve. Please, help me! 1. Prove or disprove if U, V, W are subspaces of V for which U (dir sum) W = V (dir sum) W then U=V Thank you in advance!