Let T be the Lin. Trans. $\displaystyle p_2 \rightarrow p_2$ defined by

$\displaystyle T(at^2+bt+c) = (3a+2c)t + (2b-5c)$

1.) Determine a basis of the kernel of $\displaystyle T$

2.) Determine a basis of the range of $\displaystyle T$

3.) Is $\displaystyle T$ onto? Is $\displaystyle T$ one-to-one? Explain!

....

Well for #3 I know one-to-one has to do w/ range and onto has to do w/ kernel...

Some help?