Originally Posted by

**M.R** Hi,

I am trying to prove the following are not a linear transformation:

1. $\displaystyle T: R^3 -> R$ defined by $\displaystyle T(x) = x_{1}x_{2}x_{3}$

2. $\displaystyle P -> P, T(p)=p+2p'+3p''$, where P is the vector space of polynomials (of any degree)

3. $\displaystyle det: M_{22} -> R, det \left(\begin{array}{cc}a&b\\c&d\end{array}\right) = ad-bc$

My attempt:

I have tried the 0 vector & -1 scaler multiplication and it staisfies all the 3 eqations. Furthermore they satisfy addition as well. So why are they not linear transformation?