ENG1091 Mathematics for Engineering Assignment 2 - User Web ...

SCHOOL OF MATHEMATICAL SCIENCES
ENG1091
Mathematics for Engineering
Assignment 2: Linear Equations and Matrices
Due date: Lab class for week 4
There are two questions in this assignment worth a total of 30 marks (5% of the final
mark for this unit).
The first question (15 marks) is an exam style question.
The second question (15 marks) is a traditional assignment style question.
The questions will be marked using distinct criteria as detailed in the unit-guide and in
the examples on the unit website. Please read these carefully.
For full marks you will need to show all of your working.
Late submissions will be subject to late penalties (see the unit guide for full
details).
Short answer exam style question
1. (a) Use Gaussian elimination with back-substitution to find all solutions of the following
system of equations. Be sure to record each row operation (e.g., R 2 ← 2R 2 − R 1 ).
4x + y − 2z = 4
x − 2y + z = 1
x − 3y + 2z = 3
4/15
(b) Evaluate each of the following
⎡ ⎤
2 1 [ ]
(i) ⎣ 4 3 ⎦ 1 5
, (ii)
3 1
2 6
(c) Let
⎡
⎣
2 4
1 7
1 4
A =
⎤
⎦
[ 1 7
2 4
[ 4 3 1
3 4 1
]
.
]
⎡
, (iii) det ⎣
1 7 2
2 1 6
4 2 1
⎤
⎦.
3/15

School of Mathematical Sciences
Monash University
Find numbers a and b such that
aA 2 + bA − 10I =
[ 0 0
0 0
where I is the 2 by 2 identity matrix. 4/15
(d) Use the result of the part (c) to compute the inverse of A. 4/15
]
,
Detailed answer assignment style question
2. The simplest electrical circuit would have to be a resistor connected to a battery. If
somebody asked you to compute the current through the resistor you would need go no
further than Ohm’s law, V = IR. So much for simple circuits. But for circuits like the
following
things are not so simple. In this case we need to use Kirchoff’s laws which state that
◮ The total change in electrical potential around a closed loop is zero.
◮ The sum of all currents at any node in the circuit is zero.
So for the above circuit we could write down a number of equations. Here are two of
them
0 = i 2 R + i 7 R − V
0 = i 2 − i 3 − i 7
Your job is to construct the remaining equations and then solve for the seven currents
i 1 to i 7 in terms of V and R. 15/15
16-Feb-2014 2