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    Linear Algebra

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    Ideals for Intersections

    Please answer each part in full: Let I and J be ideals of R: (a) Prove that I+J is the smallest ideal of R containing both I and J; (b) Prove that IJ is an ideal contained in I (intersection) J (c) Give an example where IJ is not equal to I (intersection) J (d) Prove that if R is commutative and if I+J=R, then IJ

    Graph and Solve Linear Equations

    See the attached file. 1.) How do you draw a line whose x- intercept is -7 and whose y-intercept is -6? 2.) How do you graph the line with equation y=-2x? 3.) How do you graph the line 2x+2y=13? 4.) How do you graph a line with the slope of -3 passing through the point(2,4)? 5.) How do you find a slope of a line w

    Inequality and line equation

    1.) The price of a personal computer is $2000. The markup is $150. What is the dealer cost? 2.) Solve the inequality 4y - 7 > 9y - 2. Use set-builder notation. 3.) Graph using slope and y-intercept method of y = (3/2)x - 3 4.) Graph using slope and y-intercept method of 5x + 5y = 10 5.) Graph the inequality

    Linear Equations and Solving Equations

    The function that relates weight in grams of a crystal (w) to the temperature t in degrees Fahrenheit in which it was grown is as follows (fictitious): W(t) = 0.8t + 12 Find w(-6). a. impossible to tell from info given b. less than 8 grams c. at least 8 grams but less than 10 grams d. at least 10 grams but less t

    Systems of Equations with Three Variables and Real-Life Applications

    Hello again ! trying to solve for x and Y in the following problems. please explain 1. a. X + Y=6 ; 2X + Y =8 b. 7X + 3Y=14 ; 5X + 9Y= 10 c. 4X + Y= 16 ; 2X + 3Y= 24 d. 12X + Y= 25 ; 8X - 2Y= 14 2. Suppose Bob owns 8000 shares of company X and 6000 shares of Company Y. The total value of Bobs holding of these

    MATLAB Signals Theory- Linear Time - Inveriant Discrete Time System

    A linear time-invariant discrete-time system has transfer function h(z)=((z^2)-z-2)/((z^2) + 1.5z-1) a. Use MATLAB to obtain the poles of the system. Is the system stable? Explain. b. Compute the step response. This should be done analytically, but you can use MATLAB commands like conv and residue. c. Plot the first seve

    Basis and Dimension, Eigenvalues, and Eigenvectors and Diagonalizability

    Text Book: - Linear Algebra, Author: - Insel, 3rd Edition Following questions to be answered In page Number: - 52 & 53 : Questions: - 12, 21 In Page Number :- 54 :- Question :- 25 In page Number: - 247 :- Question : - 2 / c, d In Page Number: - 248 & 249 : - Question: - 3/ b,c. 4, 8/a, 11/a, b. 12/a In Page

    Differential Equations : Bifurcations in Linear Systems

    In Chapter 3, we have studied techniques for solving linear systems. Given the coefficient matrix for the system, we can use these techniques to classify the system, describe the qualitative behavior of solutions, and give a formula for the general solution. In this lab we consider a two-parameter family of linear systems. The g

    Solving Systems of Equations

    1. Solve each system by graphing. y = - 2/3 x 2x + 3y = 5 2. Solve each system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. 2x - y = 4 2x - y = 3 3. Write a system of two equations in two unknowns for each problem. Solve each system by substation.

    MATLAB Signals - Conv and Transfer Function of System

    1. A discrete-time system has the following unit-pulse response: h[n] = 0.5^n - 0.25^n for n >= 0 Correspondingly, the following difference equation describes the behavior of the system: y[n + 2] - 0.75y[n +1] + 0.125y[n] = 0.25x[n +1] a. Use the MATLAB command conv to calculate the response of the system to a unit ste

    Systems of Linear Equations and Inequalities

    I am at a total loss on these. Any assistance you could give me would be greatly appreciated. I have a total of 9 problems. Thanks a lot!! The start-up cost for producing widgets is $449, and each widget costs $91 to produce. What is the equation for this situation? Use X for # widgets produced and Y for cost. a. none of

    Systems of Differential Equations with Zero Eigenvalues

    From Special Cases: Repeated and Zero Eigenvalues. Please show each step of you solution. There is no need for drawing graphs for me, but if you do it, I will appreciate it. Thank you. Please solve for only #18. Don't need for graph comparison with previous exercise in part (f), but if you can provide graphs for only this pr

    Systems of Differential Equations

    From Special Case: Repeated and Zero Eigenvalues. Please show each step of your solution. You do not need to do part (c), but if you can provide a graph for only this problem, I will appreciate it.

    Acute, Obtuse, Right or Straight Angles.

    1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) A. By looking at the picture, do you think is an acute, obtuse, right, or a st

    An art dealer sold two artworks for $1520

    An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% profit on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork. A professor starte

    State-Space Representation

    Consider the system defined by: (see attached file) where y is the output and u is the input of the system. Obtain a state-space representation of the system.

    Linear, Time-Varying, System

    a) Show that the linear, time varying system x =A(t)x is asymptotically stable if xT A(t)x < - &#949; for all x &#8800; 0 and all t &#8805; 0 and some &#949; > 0. Hence show that the system -8/5+3/5sin t

    Finite Dimensional Space and Nullity

    Let V be a finite-dimensional real (i.e. F = R) vector space. Let T be an element of L(V)(set of operators on V), and assume that T^2 = 0. a) Prove that rangeT is contained in nullT. b) Prove that dimnullT >= (dimV )/2. Hint. Make use of a).

    Complex n-Tuples, Basis and Diagonalization

    Let T be an element of L(C^3) [complex 3-tuples] be the operator defined by T(z_1, z_2, z_3) = (z_2, z_3, z_1). a) Write the matrix of T in the standard basis of C^3. b Find all eigenvalues of T c) Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is "NO", explain why. If your

    Discussing Eigenvectors and Eigenvalues

    Assume that ST = TS. Prove that the operators S and T have a common eigenvector. Let V be a complex (i.e. F = R) finite dimensional vector space. Let S, T be elements of L(V ) (set of operators on V). Assume that ST = TS. Prove that the operators S and T have a common eigenvector. these are the steps: a) Explain why T

    Linear Equations and Systems

    #1) Write the equation y=2/3(x)-3 in standard form using only integers and a positive coefficient for x. #2) Find the equation (in slope-intercept form) of the line that goes through (-1,2) and has slope 4. #3) Solve: 4-5x > 11 #4) Solve the system of linear equations by the substitution method. Then, state

    Solutions to Linear Equations

    1. Which of the following points is a solution to this equation: y = -3x + 8 a. none of the following is a solution b. all of the following are solutions c. (0, 8) d. (1, 5) e. (-1, 11)