I have this Linear Transformation given by
Then I have to show that is linear.
I do not really have any idea... SO really need some help please!
That makes no sense at all! f is supposed to map into but you have 3 components! In addition is defined by (a,b)+ (c,d)= (a+c, b+d), "component wise".
f is a function from which, I think, is the space of polynomials of degree 3 or less with real coefficients, to R^{2}, the space of pairs of real numbers. f(P(x)) is defined as the pair (P(1), P(-2)).
So, for example, if [tex]P(x)= x^3+ 2x- 1[/itex], P(1)= 1+ 2- 1= 2 and P(-2)= -8- 4-1= -13. f(P)= (2, -13).
and . Are those the same?