SRM University AP Math Exam PDF 2024

Summary

This is a past exam paper from SRM University AP, for the Odd Semester 2024, covering Mathematics and Statistical Foundations for Machine Learning, Data Science, and Cyber Security (FIC 504, 506, 507). It includes instructions and multiple choice questions focusing on topics such as LU and QR decomposition, eigenvalues, eigenvectors.

Full Transcript

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

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