1. ## 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

2. 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.

3. 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

4. If by ‘linear’ you mean ‘linear transformation’ then the function in part (c) is not linear: note that f(0,0)=(1,1).

5. 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....... ) help please

6. 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.