
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 5th, 2017, 10:23 AM  #1 
Newbie Joined: Jan 2017 From: Nowhere Posts: 5 Thanks: 1  Find the values of a so that the operation is closed in [0;1]
I would appreciate anyone's contribution for the following exercises : 1)Find the values of a so that the operation $\displaystyle x * y = x + y  xy  ax  ay +a $ is stable in the set [0;1] //// First one was solved 2) For a=0, find a formula for $\displaystyle \overbrace{x*x*x*x* .....*x}^{ntimes} $. Last edited by MozartInACan; January 5th, 2017 at 10:46 AM. 
January 5th, 2017, 04:43 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 1,763 Thanks: 905  Quote:
$x^n = (1)^{n1}x^n + \displaystyle{\sum_{k=1}^{n1}}~(1)^{k1} \begin{pmatrix}n \\ k \end{pmatrix}x^k$ I leave it to you to prove this via induction.  
January 6th, 2017, 09:57 AM  #3 
Member Joined: Dec 2016 From: USA Posts: 46 Thanks: 11 
When $a = 0$, $\overbrace{x*x*x* \cdots *x}^{n\text{ terms}} = 1  (1x)^n$. Last edited by quasi; January 6th, 2017 at 10:06 AM. 

Tags 
closed, find, operation, values 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to find out if the subset is closed?  FightingMongooses  Real Analysis  2  June 26th, 2016 07:15 AM 
Can someone find a closed form expression for this please?  Davebungo  Calculus  0  January 13th, 2014 03:30 PM 
Is the union of infinite disjoint closed sets closed?  03sqq  Real Analysis  4  November 13th, 2012 04:40 AM 
find values of ? that correspond to the ? values?  space55  Calculus  0  October 10th, 2010 04:23 PM 
Find all the values of x  sivela  Abstract Algebra  1  January 25th, 2010 06:52 AM 