Be sure to show all your work including each step of elimination and clearly indicate your final answer. (Hand-writing)

Linear Algebra / Matrix

Math 220 Spring 2023 Written Homework 2 Be sure to show all your work including each step of elimination and clearly indicate your final answer. 1. Give a geometric description of the span. Justify your response. (b) s () Span ] [8]) 2. A thin triangular plate of uniform density and thickness has vertices at v, = (0,3). va = (4,3), and vs = (2, 1). The mass of the plate is 3 g. (a) Find the (r, y)-coordinates of the center of mass of the plate. This balance point of the plate coincides with the center of mass of a system consisting of three l g. point masses located at the vertices of the plate. (b) Determine how to distribute an additional mass of 2 g. (so that the plate has a total mass of 5 g.) at the three vertices of the plate to move the center of mass to (2, 2). 3. Let A = 3 and b = by Show that the matrix equation Ax = b does not 4 ba have a solution for all possible b and describe the set of all b for which Ax = b does have a solution. 4. During an epidemic a population is classified as susceptible, infected, or recovered. Over each 14 day period. . 5% of the susceptible population becomes infected . 40% of the infected population recovers . 10% of the recovered population becomes susceptible (a) Set up a matrix equation that models how the population transitions over each 14 day period. (b) If initially there are 1,000 susceptible, 100 infected, and 300 recovered individuals, determine the number of individuals in each category 14 days later