COMSATS Institute of Information Technology, Islamabad
Department of Mathematics
Subject: Linear Algebra (BS(mathematics)-III)
Assignment 1
Due date: 5 October 2012
Question # 1. Suppose that we want to find a polynomial f (x) of degree n−1 whose graph
passes through n given points (x1 , y1 ), ... , (xn , yn ). Show that this problem can be solved by
finding the inverse of the following matrix

1 x1
 1 x2



 . .
X=
 . .

 . .


x21
x22
.
.
.

... x1n−1
... x2n−1 



.
. 
.
.
. 

.
. 


1 xn x2n ... xnn−1
Conversely, the inverse of this matrix can be found by solving the polynomial problem for certain
special cases. Can you do this?
Question # 2.
Find the inverse of the following

1 −1 0
 a 1 1
A=
 3 0 1
1 1 1
matrix if it exists.

a
0 
,
6 
1
where a = your roll number.
GOOD LUCK
1