# linear functions

• Dec 24th 2006, 08:49 AM
0123
linear functions
which of the following functions is not linear?
a)for all x€R, f(x)=(x; 2x)
b) for all (x; y; z)€R3, f(x; y; z)=x-2y+3z
c) for all (x; y) € R2, f(x; y)= (x+1; y-1)
d) they're all linear

And why???

I hope it's clear enough to understand...These things are driving me crazy, any help is really appreciated..thanks
• Dec 24th 2006, 09:16 AM
ThePerfectHacker
Quote:

Originally Posted by 0123
which of the following functions is not linear?
a)for all x€R, f(x)=(x; 2x)
b) for all (x; y; z)€R3, f(x; y; z)=x-2y+3z
c) for all (x; y) € R2, f(x; y)= (x+1; y-1)
d) they're all linear

And why???

I hope it's clear enough to understand...These things are driving me crazy, any help is really appreciated..thanks

A linear function of a single variable is,
$f(x)=ax+b$
And several variables is,
$f(x_1,x_2,...,x_n)=a_1x_1+a_2x_2+...+a_nx_n+b$
It is just a combination of all exponents to the first power of all the variables.
Thus, the answer is the 4th choice.
• Dec 24th 2006, 10:18 AM
0123
I can't see the reasoning behind the answer(latex doesn't work) but I can tell you that the right answer is c, that is the third. But I can't see why. Any idea?thanks
• Dec 24th 2006, 10:21 AM
Plato
If by ‘linear’ you mean ‘linear transformation’ then the function in part (c) is not linear: note that f(0,0)=(1,1).
• Dec 24th 2006, 10:28 AM
0123
I am not much into this math part :( but the solution provided by the book is c. We talked of this linear functions after the matrix argument and said that f is linear when there exist a matrix such that y=Ax( and talked about homogeneity and additivity....... :confused: :confused: :confused: ) help please:(
• Dec 24th 2006, 10:37 AM
Plato
Note that f(0,0)=(1,1). To be a linear transformation we need f(0,0)=(0,0).
In each of these we can see the mappings as a linear transformation from one linear space to another. One property of linear transformations is that they map the ‘zero point’ to the ‘zero point’. That is a necessary but not sufficient property for a linear transformation.