Exam 1

  1. Question

    For the matrix
    A =( 16416-4 456-9 16633-28 -4-9-2858 ).

    compute the matrix L=( ij )1i,j4 from the Cholesky decomposition A=L L .
    Which of the following statements are true?
    1. 41 =-1
    2. 44 <4
    3. 22 =-1
    4. 11 >0
    5. 32 1

    Solution

    The decomposition yields
    L =( 4000 1200 4140 -1-4-54 )

    and hence:
    1. True. 41 =-1
    2. False. 44 =44
    3. False. 22 =2-1
    4. True. 11 =4
    5. True. 32 =1