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CSCI 510/EENG 510 Image and Multidimensional Signal Processing Homework Assignment 0 This assignment is a review of some pre-requisite topics. It is not necessary to turn it in, although you should do these problems to make sure you understand the concepts. The first four problems are a review of some mathematical concepts. You should be able to do these problems by hand, but it is ok to check with a computer. 4 − 2 . 1. Consider the matrix A = 1 1 a) Find the transpose of A b) Find the determinant of A c) Find the trace of A d) Find the inverse of A. e) Which of the following vectors is an eigenvector of A? x = (2 1)T x = (-1 2)T x = (0 1)T x = (1 0)T 2. Consider the vectors x = (1 2 3)T and y = (-1 2 -3)T. a) Compute the inner (dot) product x∙y. b) Compute the vector (cross) product x × y . 3. Consider the 8-bit binary number B = 11000001. a) Find the decimal value of B if it represents an unsigned binary number b) Find the decimal value of B if it represents a two’s complement binary number. 4. The faces of a 10-sided die are numbered 0 through 9. a) What is the probability that the value of the roll is a prime number? b) What is the expected value of the roll? c) If the die is rolled twice, what is the probability that the same number is obtained both times? 5. Matlab exercises. a) Create a matrix A, any size and shape you want, and fill it with arbitrary values. Compute AAT and ATA. The results should be square, symmetric matrices. b) Write a Matlab program to produce the first 30 Fibonacci numbers. 1