MATH V2010 Midterm: MATH V2010 Columbia S11Exam1 LinearAlgebra S11

HW14 pdf 2. (15 pts) Consider the linear homogeneous system of 2 equations and 2 unknowns, Az. The matrix A, and one pair of it's eigenvalues and eigenvectors are given (you do NOT have to rederive the eigenvalues or eigenvectors). Sketch (by hand) the phase portraits. Be sure to label your axis. A= =11-11, 0-1 1 0] 3. (15 pts) Consider the following second-order constant coefficient differential equation y"+2y' + 5y = 0 (a) (4 pts) Solve as a second-order constant coefficient equation. (b) (3 pts) Rewrite the second-order constant coefficient differential equation as a system of 2 equations and 2 unknowns, x1(t) and r2(t). Label your variables clearly. (c) (5 pts) Solve the system of equations. Write your solution in non-matrix form: Zi (t) = Z2(t) = … (d) (3 pts) Is your answer to (c) consistent with your answer in (a)? Check both ri(t) and r2(t).

GRAND CANYON UNIVERSITY MAT-154 Topic 5 Project Worksheet Please use and submit this worksheet to complete the assignment. You may use a Microsoft Excel spreadsheet for calculations, tables, and figures and then cut and paste them into this worksheet. Student Name& Student ID: State the Chemical Reaction for your ID: State the System Representation of Chemical Reaction (5 Pts.) How many solutions do you expect the system to have? Why? (2 Pts) Set up the system in matrix form to be solved in MS Excel (see the many resources on internet on solving a system of linear equations using MS Excel) and solve the system using MS Excel. (3 Pts Describe an Intuitive approach to Balancing (10 Pts) 4A F7 F5 F6

Directions: Prob lems should be solved in their entirety on separate pieces of p aper. Write your name on the upper right corner of every page that you intend to have graded. To prevent clutter, start each problem on a new page. Final solutions should be of the work for a particular problem must be shown. clearly marked. In order to qualify for partial credit, all Problem 1. (25 pts) For the following function f(x) = 4x-18-10 d and classfy all local eztrema. On uhat intervals is f (n) increasing? Decreasing? (0) Find all points of inflection. On what intervals is J(a) concave up? Concave doun? c) Using this information, sketch f(a). Be sure to label the coordinates of all local extrema or points inflection. Problem 2. (20 pts) Suppose()-6r on the interval |-2,1]. Find the global minimum and glob marimum for this curve. Show all work needed to justify your answer. Problem 3. (15 pts) The following is a graph of cost and revenue for producing some good