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

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