SRM University AP Math Exam PDF 2024

FIC 504, 506, 507 Department of Mathematics, SRM University AP Odd Semester, 2024 CLA-2 FIC 504, Mathematics and Statistical Foundations for Machine Learning FIC 506, Mathemat...

FIC 504, 506, 507 Department of Mathematics, SRM University AP Odd Semester, 2024 CLA-2 FIC 504, Mathematics and Statistical Foundations for Machine Learning FIC 506, Mathematics and Statistical Foundations for Data Science FIC 507, Mathematical Foundations for Cyber Security Semester I, Regulation 2024 Instructions ˆ Do the rough work in the provided A4 sheet. ˆ Put tick mark (✓) to your answer. ˆ Mention your name, registration number and section on the question paper. ˆ Please return your rough work along with the question paper at the end of the exam. ˆ Each question carries 2 mark. Name: Roll No.: Section: 1. Which of the following is a correct statement about LU decomposition? A. LU decomposition is used to find the inverse of a matrix. B. LU decomposition is used to solve systems of linear equations. C. LU decomposition is used to find the determinant of a matrix. D. LU decomposition is used to find eigenvalues and eigenvectors. 2. In LU decomposition, a matrix P is decomposed into which two matrices? A. P = L + U B. P = L − U C. P = LU D. P = L/U   4 3 3. Given the matrix A = , what are the L and U matrices in its LU decomposition? 6 3         1 0 4 3 1 0 4 3 A. L = ,U = B. L = ,U = 1.5 1 0 −1.5 0.5 1 0 1.5         1 0 4 3 1 0 4 3 C. L = ,U = D. L = ,U = 1.5 1 0 1.5 0.5 1 0 −1.5 4. Which of the following is a correct statement about QR decomposition? A. QR decomposition is used to find the inverse of a matrix. B. QR decomposition is used to solve systems of linear equations. C. QR decomposition is used to find the determinant of a matrix. D. QR decomposition is used to find eigenvalues and eigenvectors. 5. In QR decomposition, a matrix M is decomposed into which two matrices? A. M = Q + R B. M = Q − R C. M = QR D.M = Q/R   3 2 6. Given the matrix A = , what are the Q and R matrices in its QR decomposition? 4 6         −3/5 −4/5 5 6 3/5 4/5 6 5 A. Q = ,R = B. Q = ,R = 4/5 3/5 0 2 −4/5 −3/5 2 0         3/5 −4/5 5 6 3/5 −4/5 5 6 C. Q = ,R = D. Q = ,R = 4/5 3/5 0 2 4/5 3/5 2 0 7. Which of the following is a correct statement about eigenvalues? A. Eigenvalues are the solutions to the characteristic equation of a matrix. B. Eigenvalues are the solutions to the determinant equation of a matrix. C. Eigenvalues are the solutions to the inverse equation of a matrix. D. Eigenvalues are the solutions to the transpose equation of a matrix. FIC 504, 506, 507 Page 1 of 2  8. Which of the following is a correct statement about eigenvectors? A. Eigenvectors are vectors that change direction under a linear transformation. B. Eigenvectors are vectors that do not change direction under a linear transformation. C. Eigenvectors are vectors that change magnitude under a linear transformation. D. Eigenvectors are vectors that do not change magnitude under a linear transformation.   2 0 9. Given the matrix A = , what are its eigenvalues and eigenvectors? 0 3         1 0 0 1 A. Eigenvalues: 2, 3; Eigenvectors: , C. Eigenvalues: 2, 3; Eigenvectors: , 0 1 1 0         1 0 0 1 C. Eigenvalues: 3, 2; Eigenvectors: , D. Eigenvalues: 3, 2; Eigenvectors: , 0 1 1 0 10. Which of the following methods can be used to find eigenvalues and eigenvectors? A. Gaussian elimination B. LU decomposition C. QR decomposition D. Gauss-Jordan method —————————-end of the question paper —————————- FIC 504, 506, 507 Page 2 of 2