Kernel Problem - # 3

[Jason76]

Find the kernel of the linear transformation.

\(\displaystyle T_{3} \rightarrow R, T(a_{0} + a_{1} x + a_{2} x^{2} + a _{3} x^{3})\)

The answer is "\(\displaystyle a_{1}x + a_{2}x^{2} + a _{3}x^{3}): a_{1}, a_{2}, a_{3}\) are real" However, more reasoning might be needed to show how to get there.

 

[stapel]

Find the kernel of the linear transformation.

\(\displaystyle T_{3} \rightarrow R, T(a_{0} + a_{1} x + a_{2} x^{2} + a _{3} x^{3})\)

The answer is "\(\displaystyle a_{1}x + a_{2}x^{2} + a _{3}x^{3}): a_{1}, a_{2}, a_{3}\) are real" However, more reasoning might be needed to show how to get there.

Um... no reasoning at all is shown so, yes, more reasoning is definitely needed.

How did you arrive at your solution? Try writing out what you thought and computed. This should provide the necessary "reasoning".