MTH501 Assignment No1

MTH501 Assignment No. 1 Student ID : BC170201241 Question No. 1

 2    For what value of k  ,  kA  kA 1, where  A  1 .    1  t 



Given  :-

 2    A = 1     1    ( kA) t  ( kA)  1 To  Find :k = ? Solution :First we will find (kA)

 2  A = 1      1    2k   k   kA       k    ( kA) t  

 2 k 

k -k   

We  know that (kA (k A) t (k (kA A)=1 )=1 Put the vaules

 2k  = 1  2k k -k     k      k    2 2 2   4k  + k + k   =1 6k 2  1 2

k 



1

6 Taking  square root on both sides k 2  k  

1 6

1 6

So  the value of k is

1 6

QUESTION No. 2 Determine the condition on   , so that the Echelon and reduced Echelon form of

 sin    cos   Given

cos   

 holds.

sin   

:-

sin    cos   To  Find    =

cos  



sin   :-

?

Solution  :-

sin    cos 

First we will make echelon form of 

cos  

 by

sin  

Divi Di vidi ding ng row row 1 wit with h sin sin , we wil willl get get

1   cos  

cos  / si s in   

 Add  Cos  Cos

sin 

 

and th then di divide (s (sin +cos ) wi with ro row 2

cos / si s in    1   cos   cos  sin  cos       cos / si s in   1  0  (sin   cos  ) / ( sin  cos  )   1 cot   0 1   ( sin  / cos   tan  & 1/tan =cot )   The  above

 

condition satisfies the echelon form

 Now for Reduced echelon echelon form cot  must be equal equal to zero cot  = 0    =

cot 1 (0)

   =  /2

[

cot( /2) = 0 

  /2

= cot 1 (0)]