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Linear Algebra

Linear Equations

Determine if the given ordered pair is a solution to the equation: 4. -3x + y = -2 (0,2) 6. 2x - y = -3 (-2, -1) Find the specified values: 8. 6x - 3y = 12 x-intercept & y-intercept 10. 4x - 2y = 6 slope & y-intercept Re-write the equations in the specified form: 12. y = 2x -3 write in standard form

Vectors : Linear Transformations

The following questions are from "Linear Algebra" textbook. Page 52: - Question Number: - 5,7,8,9. Page 54: -Question Number: - 27/b, 28, 29 Page 70: - Question Number: - 14, 15 & 17 Please mention each and every step. Thank you

Graphing Linear Equations

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 with coordinates (18,13) and

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

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

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

Linear Operators : 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

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)

Applications of Linear Equations

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