BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI - K.K. BIRLA GOA CAMPUS Mathematics-2 Tutorial–1

1. Use the Gaussian elimination method to solve each of the following systems of linear equations: (a) −5x1 − 2x2 + 2x3 = 14 3x1 + x2 − x3 = −8 2x1 + 2x2 − x3 = −3 (b) 3x1 − 2x2 + 4x3 = −54 −x1 + x2 − 2x3 = 20 5x1 − 4x2 + 8x3 = −83 2. Find the quadratic equation y = ax2 + bx + c that goes through the points (3, 18), (2, 9) and (−2, 13). 3. Use the Gauss Jordan method to determine the complete solution set for the given system, and give one particular nontrivial solution. −2x1 − 3x2 + 2x3 − 13x4 = 0 −4x1 − 7x2 + 4x3 − 29x4 = 0 x1 + 2x2 − x3 + 8x4 = 0 4. Prove that the following homogeneous system has a nontrivial solution if and only if ad − bc = 0: ax1 + bx2 = 0 cx1 + dx2 = 0 . 5. Find all values of a for which the resulting linear system has (a) no solution, (b) a unique solution, and (c)inﬁnitely many solutions. (i) x+y−z =2 x + 2y + z = 3 x + y + (a2 − 5)z = a (ii) x+y =3 x + (a2 − 8)y = a

6. Find an equation relating a,b and c so that the linear system: x + 2y − 3z = a 2x + 3y + 3z = b 5x + 9y − 6z = c is consistent for any values of a,b and c that satisfy that equation. 7. Show that if u and v are solution to the linear system Ax = b, then u − v is a solution to the associated homogeneous system Ax = 0. 8. If A is an n × n matrix, the homogeneous system Ax = 0 has a nontrivial solution if and only if A is singular. 9. Find all values of a for which the inverse of

1 1 0

A= 1 0 0 1 2 a exists. What is A−1 ? 10. For what values of λ does the homogeneous system (λ − 1)x + 2y = 0 2x + (λ − 1)y = 0 have a nontrivial solution?

...ACCG399 Tutorial 1 – Week 2
Thought Activity
Accounting, from my conception, is a system that provides quantitative information about finances. Unlike accounting, accountability is a responsibility to someone or for some activity. However, an accountant is an occupation who maintains and audits business accounts.
Have been studying in university nearly two years, I have come to some conclusions about accounting. Until now, the thing that I enjoy is in financial accounting,...

...teacher.
In order to avoid the evils of private tuition, educational institutions themselves may arrange tutorial classes. If the regular teachers cannot attend to the tutorials special tutors may be appointed to attend to very small groups of needy students. Such contacts may help build confidence in the student. Such tutorial classes may be complementary as well as supplementary. The tutorial system when properly organised will go a...

...School of Business and Economics
Loughborough University
Module 13ECP104 Semesters 1 and 2
RESEARCH COMMUNICATION
This Module Guide is available on the Learn Server.
VERY IMPORTANT: READ ALL OF THIS GUIDE
Semester 1
Lectures and Tutorials: Fridays (detailed timetable on pages 9 and 10 of this guide)
Lecturer & Tutor 1: Dr Lawrence A. Leger
Sir Richard Morris Building: Room BE 2.14
Email L.A.Leger@lboro.ac.uk
Telephone 222716
Office Hours:...

...1 Tutorial Schools, The Better Place to Learn?
It is not surprising to see hordes of students busy checking their shopping list at counters of tutorial schools. They pay more respect to the teaching materials offered by tutorial schools than those by their day time school. Are tutorial school so magical as thought by them? Can tutorial classes really help or they are just help use students' money? Lets explore the pros...

...Survey for Tutorial Agency Greetings! We are fourth year accountancy students from the University of the Assumption working on our feasibility study for agency offering tutorial services. Please help us through filling out this survey form. Kindly put a check mark on your answers. Thank you for your participation. Child’s Information Name: Address: School: Grade Level: Age: Gender: ___ Male ___ Female
Questions Related to the Study 1. Do you believe in the...

...USE 0F SEMINARS AND TUTORIALS AS A STUDY STRATEGY
SEMINAR
A seminar is a small group meeting in which students and tutors discuss information on a chosen topic. They provide opportunity to explore topics by discussion and to identify and sort out any problem.
It’s a teaching-learning approach conducted as follows;
Students (experts) are given topics in advance to prepare for their seminar paper by researching
The seminar paper is presented orally
There is a session for the...

...COURSE 2 - The Balance Sheet
The balance sheet (also called statement of financial position) reports the financial position of the business at a point in time. It does so by listing the categories and amounts of assets, liabilities and equity on a specific date, in a format that proves the fundamental accounting equation.
ASSETS = EQUITY + LIABILITIES
or
ASSETS – LIABILITIES = EQUITY
Formats of...