Find the kernel of the linear transformation.
\(\displaystyle T
_{2} \rightarrow P_{1}, T(a_{0} + a_{1} x + a_{2} x^{2} ) = a_{1} + 2a_{2}x = a_{0}\)
The answer is "\(\displaystyle a_{0} :a_{0} \) is real" However, more reasoning might be needed to show how to get there.
\(\displaystyle T
_{2} \rightarrow P_{1}, T(a_{0} + a_{1} x + a_{2} x^{2} ) = a_{1} + 2a_{2}x = a_{0}\)The answer is "\(\displaystyle a_{0} :a_{0} \) is real" However, more reasoning might be needed to show how to get there.