Describe at least three distinct ways to solve a system of equations using linear algebra. (Distinct means that the approach is fundamentally different.) Be specific and detailed using linear algebra vocabulary. It might be helpful to pick an example problem and illustrate each of the three methods.  

Suppose T1 and T2 are linear transformations from Rn to Rn. Let T(x) = T2(T1(x))

The responses should be very clear like you are writing instructions to someone who doesn’t know the process.  

1. Describe how to find the transformation matrix of T1.

2. Describe how to find the transformation matrix of T. (Bonus +2 points if you can describe a second method.)

3. Is T2(T1(x)) = T1(T2(x)) for any linear transformation T1 and T2? Explain.

Please solve the following equation by using the frobenius method.

xy′′ − (3 + x)y ′ + 2y = 0

My apologies, the original image did not upload properly.

Unoccupied seats at the Cardinal’s football stadium causes the football team to lose revenue. The Cardinal’s owner wants to estimate the mean number of unoccupied seats per game over the past few years. To accomplish this, the records of 225 games are randomly selected and the number of unoccupied seats is noted for each of the sampled games. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats. x-=

Compute all possible cycles, length of the cycle, and number of cycles in the following cases:

(a) mult by 3 mod 17

(b) mult by 13 mod 17

(c) mult by 9 mod 17

(d) mult by 16 mod 17

A leading UK Chocolate Brand has seen a downturn in sales due to new competition in the

market. Analysis work has shown the need for a customer loyalty programme. You have been

tasked with designing the approach that your Partner will present to the Client.

One Page Project Summary including;

▪

The purpose of the assignment and the outline of the

task

▪

The core deliverables expected from the engagement

▪

The make up of your Consulting Delivery Team

One Page High

-

Level market summary, including;

▪

The market size

▪

Core competition in the market

▪

Challenges faced by the industry

One Page Solution Overview, including;

▪

Your proposed solution to the problem statement

▪

Your justification for your solution

▪

Expected outcomes / ROI if the Client goes ahead with

your suggestion

One Page Implementation Plan, including;

▪

A One Page Project Plan

▪

Your change management approach to ensure

seamless integration

Explain what is rule based system and the fuzzy expert system based on the following information. Here is what Amy will do. When the temperature is cold, she will wear a coat. When the temperature is moderate, she will wear a jumper. When the temperature is cold, she will stay indoor. When the temperature is moderate, she will go for shopping. Here is Amy’s consideration for the weather/temperature. It is cold when the temperature is below 16 degree. It is moderate when the temperature is between 16 – 22 degree.

The diagram shows a kite AFCE inside rhombus ABCD. Angle AFB = angle AED = 35degrees, angle ABF = angle ADE = 120degrees. Find the size of angle EAF.  

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show that there exists a point c ∈ (0, 2π) such that cos(c)f(c) + sin(c)f'(c) = 2 sin(c).

In this activity we have graphed the function y = sin(x). For this assignment, you will explore the changes that occur in the curve when we make simple changes to the function.

For each of the different parts below, create sketches and a description of the crucial properties of the periodic graphs including:

• Period
• Amplitude
• Maximum
• Minimum
• Axis of the Curve
• Zeros

Finally, in a few sentences, based on your findings describe how these changes in the function affect the properties of the curve.

For your sketches, you can scan hand-made sketches and email or fax these to your instructor. Alternately, you may use a simple drawing program like Windows Paint.

Consider the optimization problem of the objective function f(x, y) = 3x 2 − 4y 2 + xy − 5 subject to x − 2y + 7 = 0. 1. Write down the Lagrangian function and the first-order conditions. 1 mark 2. Determine the stationary point. 2 marks 3. Does the stationary point represent a maximum or a minimum? Justify your answer.

Find the particular integral of the differential equation

d²y/dx² + 3dy/dx + 2y = e ^−2x (x + 1). show that the answer is yp(x) = −e ^−2x ( 1/2 x² + 2x + 2) ]