Answers to Linear Algebra Quiz
  1. 2 seconds for 5 computers

  2. q1 = ( 0 1 0 0 0 0 0 0 1 0 )T and q2 = ( 1 0 1 0 0 1 1 0 0 0 )T

  3. 8,000,000 seconds ≈ 92.6 days

  4. PrecisionA = 29/39 ≈ .7436, RecallA = 29/45 ≈ .6444, PrecisionB = 25/31 ≈ .8065, RecallB = 25/45 ≈ .5555

  5. The recall in this case would be greater than 1, which doesn't make much intuitive sense. The precision would be equal to 1. Despite the high scores, this search engine would not be very good.

    1. dist(h,i) = √(41)

    2. length(x) = √(17), length(y) = √(89)

    3. length(x) = √(107)

  6. θ ≈ 42.71°

  7. MATLAB commands:

    [U,D,V]=svd(A);
    A4=U(:1,:4)*D(1:4,1:4)*(V(:,1:4))';
    A3=U(:1,:3)*D(1:3,1:3)*(V(:,1:3))';

  8. MATLAB commands:

    B= rand(200,300);
    [U,D,V]=svds(B,10);

  9. MATLAB commands:

    P=gallery('frank',10,1);
    Q=gallery('frank',30,1);
    [Up,Dp,Vp]=svd(P);
    [Uq,Dq,Vq]=svd(Q);
    plot(diag(Dp);
    plot(diag(Dq);

  10. MATLAB commands:

    Ep=P-Pk;
    normEp=norm(Ep,2);

    Relative errors are more appropriate here.