Section A
(Answer all questions -- do not spend more than 1 hour)
Each question carries
2
marks.
• A
1.
Create a list
of
tuples containing the name and age of five imaginary friends.
• A2. Using (!) or otherwise, use a bash command
to
output the string, "This
is
a programming lab course!"
•
A3
.
Define a
recursive
function for f
(x)
=
x
! ,
where
X
!
==
I
*
2
*
3
* ...
x
and f
(0)
=
1.
Print the output for f (
10).
• A4. Using a single line statement, create a random 2 x 2 matrix
A
with elements between 0 and 5.
You
can include
an
additional
import
statement.
• A5. Create a list from an array
of
100 real numbers between 0
and
1. Extract the last five numbers.
•
AG.
Define a function that calculates the trace and determinant of a 2 x 2 matrix
A,
and returns a tuple at the output, i.e
.,
output
is
(Tr(A)
,
det(A)).
Section 8
(Answer any 3 question
--
do not spend more than 45 mins
on
each)
Each question carries 6 marks.
•
81.
From linear algebra (and from elementary quantum mechanics), we know that all Hermitian matrices have real eigenvalues. However,
not all Hermitian matrices have positive eigenvalues
(A;
~
0,
V
i).
a) Write a function that checks
if
a random 2 x 2 matrix
is
Hermitian, both Hermitian and positive or neither.
(3
Marks)
Hint: Use the
numpy
(as
np)
function
np.round(x,
10)
to
round
x
to
nearest
10
decimal points, and eliminate any small imaginary part that
remains due
to
numerical error. Moreover, the commands np.real and np.imag can be used
to
isolate real and imaginary parts. Use the
fact that
for
real eigenvalues, the imaginary part must be equal
to
0.
