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January 21st, 2017, 05:56 PM  #1 
Newbie Joined: Jan 2017 From: Pakistan Posts: 4 Thanks: 0  How to solve this problem?
Let L:R>R be defined by L(u)=au+b where a and b are any real numbers. Find all values of a and b so that L is a linear transformation. "Absolute honesty isn't the most diplomatic, nor the safest form of communication with emotional beings" Last edited by skipjack; January 21st, 2017 at 07:57 PM. 
January 21st, 2017, 06:04 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,493 Thanks: 752 
a linear transform $f(x)$ has the properties that $f(x+y) = f(x)+f(y)$ $f(\alpha x) = \alpha f(x),~\alpha \in \mathbb{R}$ apply these to $L(u)=a u + b$ to determine which $a,b$ make $L(u)$ linear 
January 21st, 2017, 06:36 PM  #3  
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,493 Thanks: 752  Quote:
$L(u)+L(v) = a u + a v + 2b$ so what must the value of $b$ be in order for $L$ to be linear? when $b$ is set to this value the second property is trivial to prove.  

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