Are These Mappings True Linear Operators?

[jesuslovesu]

[SOLVED] Linear Operators

Oops, nevermind I figured out my mistake.

Homework Statement

Determine which of the following mappings T: P1 -> p1 over R are linear operators.
1) T(a0 + a1x ) = a0*x
2) T(a0 + a1x ) = a1a0 + a0*x

The Attempt at a Solution

My book states that if U = V (vector spaces) then the linear transformation T: U->U is called a linear operator on U.

So that works for the first problem; however, the second which is also P1 -> P1 is NOT a linear op(according to the answer key)... so I am a bit confused as to why that is.

 

[kurt.physics]

Answer-1) This is not a linear operator because it does not satisfy the condition that T(u + v) = T(u) + T(v).2) This is a linear operator.