Machine Learning Algorithm Comparison: SVM vs. Naive Bayes - Prof. Alfred Andrew, Exams of Linear Algebra

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                                            ! " " " " " " # $ %       ! " " " " " " # $       ! " " " " " " # $ % &('() * +, -. Name Final Exam Math 4305 2 August 2005 Andrew Page 5 of 6 c. We now redo part a, replacing A with the right 2 by 2 corner of B. 1 0 0 &=|0 Ya Ye 0% Xp 4. a. Simply multiply the given vectors by A and observe! b. Since the first and last columns are multiples of eachother, 0 is an eigenvalue. The fifth column is obviously an eigenvector for 4, sot the eigenvalues are 4, 4, 8, -4, and 0. c. p(A) =A(A-4)? (A-8)(A+8) 0200 1 02 0 2 0 d. Yes, A is diagonalizable. One possibilityis S=|0 1 1 -2 0} andD the 0-11 0 0 1041 1 1 diagonal matrix with diagonal elements 4, 4, 8, -4, 0, in that order. e. The determinatnt of A is 0, since A is singular. 5. a. Azt 2 - OoW 01 2 0 05 b. The eigenvalues of A are 1, 3, and 2. The columns of Q must be orthonormal eigenvectors for A. g =u? +3v?+2w c. The minimum value of q is the smallest eigenvalue, 1. d. The maximum is the largest eigenvalue, 3. 
         
        
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