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
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,
Originally Posted by 0123
And several variables is,
It is just a combination of all exponents to the first power of all the variables.
Thus, the answer is the 4th choice.
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
If by ‘linear’ you mean ‘linear transformation’ then the function in part (c) is not linear: note that f(0,0)=(1,1).
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:(
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.