University | Singapore University of Social Science (SUSS) |
Subject | MTH319: Mathematical Methods I |
Question 1
Given a system of linear equations as:
(a) Using matrix row operations, solve for the solution of the above system.
(b) Describe the system in terms of its linear independence, consistency and rank. What does the solution represent?
(c) Hence, determine the vector equation of a line that is normal to:
and contains the solution from Question 1(a).
Question 2
Figure Q2 below shows 5 data points being plotted. We want to find a best-fit line passing through these data points.
Figure Q2
(a) Using linear regression by minimizing the sum of squared errors, show that the equation of the best-fit line for the above data points is:
(b) Calculate the sum of squared errors for the best-fit line given in Question 2(a).
(c) Hence, determine the vector equation:
which also represents the same line given in Question 2(a). Note that there is no unique answer.
Question 3
Given the matrix A below:
Compute the eigendecomposition of A.
Question 4
(a) Classify the following DEs. For each DE, state its (i) type (PDE or ODE), (ii)
solution function, (iii) order, (iv) linearity and (v) homogeneity.
(b) Show that the function:
is a solution to the differential equation:
(c) Obtain the particular solution of the IVP below, in which k is a const
Determine the particular solution of the IVP below, where β, ∝ and Q are constant parameters
Question 5
The populations of two species, P1(t) and P2(t), are governed by the system of ODEs: where a and b are positive constant parameters.
(a) Determine the general solution of the system above.
(b) Given the information below, determine the particular solution.
(c) For your solution in Question 5(b), sketch P1(t) and P2(t) for t ≥ 0 and P1, P2 ≥ 0. What can you observe about the two species?
Stuck with a lot of homework assignments and feeling stressed ? Take professional academic assistance & Get 100% Plagiarism free papers
Get the best help with college assignments on MTH319: Mathematical Methods I. At Singapore Assignment Help we have a team of native assignment experts who have the capability to offer faultless solutions on math assignment at an extremely low price.
Looking for Plagiarism free Answers for your college/ university Assignments.
- ComfortDelGro Organisational Design Assignment Report: ESG Alignment with UNGC Principles & Sustainability Strategy
- Bomb Threat Management Assignment: Incident Response Plan for High-Risk Facilities in Singapore
- Security Concept Plan Assignment Report: International School Campus Protection Strategy at Jurong East
- CM3065 Intelligent Signal Processing Assignment Report: Midterm Exercises on Audio Captcha, Steganography & Speech Recognition
- BUS306 Risk Assessment Case Study: Outback Retail Ltd Audit Strategy and Substantive Testing Plan
- PSB6013CL Digital Marketing Strategies Project: Exploring Consumer Purchase Intentions in the Fashion E-Commerce Industry
- FinTech Disruption Assignment Report: Case Study on Digital Transformation in Financial Services Industry
- Strategic Management Assignment : Netflix vs Airbnb Case Analysis on Competitive Strategy and Innovation
- Strategic Management Assignment Report: Unilever Case Study on Industry Analysis and Growth Strategy
- PSB6008CL Social Entrepreneurship Assignment Report: XYZ Case Study on Innovation and Sustainable Impact