### Linear, Time-Varying System

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

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

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)

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

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

#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

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)

How do I go about plotting a graph with the equations of 2x+4y=10 and 3x+6y=12 and finding the intercepts?

Please see the attached file for the fully formatted problems.

The director of a summer day camp estimates that 120 children will join if the camp fee is $250, but for each $25 decrease in the fee, five more children will enroll. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the lin

From Properties of Linear Systems and the Linearity Principle. Please solve for only #27 and 28. Please explain each step of your solution. Thank you.

Given the following 3X3 matrix find the eigenvalues and eigenvectors. Please solve by hand before checking with a computer program! [(5,0,2),(0,3,0),(2,0,5)]

Please see attached file for full problem description. Solve system by the substitution method. 1. y = 2x - 6 y = x - 5 2. 7x - 4y = 26 y = x - 5 ------------------------------------------------------------------------------------ Solve each system by the addition method. If there is no solution or an

Please see the attached file for problems: D - G.

Please see the attached file for all of the problems. 12. Rose's garden is in the shape of a trapezoid. If the height of the trapezoid is 16m, one base is 20m and the area is 224m2, find the length of the other base. 13. The sum of two consecutive integers is 145. Find the two integers. 14. Yuri has a board that is 98

Please see the attached file for the fully formatted problems.

Please see attached file for full problem description. 1. Two cars leave a restaurant at the same time and travel in opposite directions. One averages 50 miles per hour and the other averages 40 miles per hour. After how long will they be 216 miles apart? 2. How many gallons of a 4% acid solution should be mixed with 2

This problem is #8 from pg. 84 of Hoffman & Kunze Linear algebra. Please see the attached file for the fully formatted problem.

This problem is #6 from pg. 83 of Hoffman & Kunze Linear algebra. A thorough explanation of the problem would be greatly appreciated. Thanks!

Text Book: - Matrix Thoery, Author: - Ortega James. M In page number 72 & 73 i need following questions to be answered. Exercise 2.3 Question numbers: - 3/b, 4, 6, 8, 9, 10, 11, 12 & 13. I request please mention each and every step.

1. solve the following equations and show work. 2. You are given the following system of linear equations: x - y + 2z = 13 2x + xy - z = -6 -x + 3y + z = -7 a. Provide a coefficient matrix corresponding to the system of linear equations. b. What is the inverse of this matrix? c. What is the transpose of this mat

Please solve for x, y & z using the process of elimination method (non matrix method) -.619x + .1648y - .2121z = 0 -.7619x - .8791y - .9697z = 0 .1905x + .4396y - .1212z = 0

Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires $12 in computer resources to process and 22 minutes of the accountant's t

1. A single-loop negative feedback system has a loop transfer function. GH(s) = K(s+2)^2 / s(s^2+1)(s+8) Determine the range of the gain K for which the system is stable. Choose either a. 23 < K < 367 b. K > 14 c. 0 < K < 5 2. A system has a characteristic equation q(s) = s^4 +9s^3 +45s^2 +87s +50 +0. De

All vector spaces are finite dimensional 1) Let X be a finite dimensional linear space. Show that, for every subspace Y of X, Y perp perp = Y (that is, the annihilator of the annihilator of Y is Y) 2) X = U = V = polynomials in s, T=d/ds, S=multiplication by s Show that S and T are linear and ST is not equal to TS

Complete the coordinates of x+2y=1 (0, ) (-2, ) (2, ) Find the slope of the line through the points (0, 4) and (5, 0) Find the slope and the y-intercept for theline y= - x+5

See attached file for full problem description. 1. Solve -3[5+2(-7+x)+x]=-3x-(x+3). 2. Solve -(4x+4)/5 = (5x -1)/2 - x/3. 3. A real estate broker's base annual salary is $18,000. She earns 3% commission on total sales. How much must she sell in real estate value during the year to earn $65,000? Set up an equation and

1. The Copperfield Mining Company owns two mines, each of which produces three grades of ore-high, medium, and low. The company has s contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore d

1. True or False: The ordered pair (-4, 5) is a solution of the following system of equations: 3X - 4Y= -32 -7X + 10Y = 78 2. Which one is addition method and which one is substitution method? (20x -3y = 14) and (4x + 10y = -8) or (x = 3y + 14) and (4x + 10y = -8) 3. What is the slope of the line pa

1. Write an equation of the line that passes through (0, -4) and is parallel y = (3/4)x + 2. Write the answer in slope-intercept form. 2. Solve the system of equations by substitution: x + 2y = 9 3x - y = 13 3. Solve the system of equations by substitution: 4x - 3y = 1 12x - 9y = 3

Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x