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- March 31st 2010, 09:02 AMbenjamin872easy? proving a linear function
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- March 31st 2010, 09:11 AMDefunkt
- March 31st 2010, 12:55 PMHallsofIvy
- March 31st 2010, 01:04 PMbenjamin872
ok but then il try say for x=1 and y=2

i find f(x+y) not equal to f(x)+f(y) which makes 10 not equal 14. so this is not linear also? can someone give me an example of a linear function that works.

......... wait so the these properties cannot be satisfied if there is a constant, but i thought a linear function could be plotted y=mx+b im confused - April 1st 2010, 03:17 AMHallsofIvy
Those are two different meanings of the word "linear". In algebra, a function of the form f(x)= mx+ b is called "linear" because its graph is a straight line.

But Linear Algebra uses a more stringent definition for "linear transformation"- we must have f(x+ y)= f(x)+ f(y) and f(ax)= af(x). As I said above, the only "linear" functions in that sense, from R to R are of the form f(x)= ax for some number a.