Enter the zero element (zero vector) for each vector space. Use the following syntax to enter your answers. Enter the vector $\langle 1,2,3 \rangle$ using $\verb+<1,2,3>+$. Enter the matrix $\left[\begin{array}{cc} 1 &2\cr 3 &4 \end{array}\right]$ using $\verb+[[1,2],[3,4]]+$. Enter the function $f(x) = x^2 - \sin(x)$ using $\verb+f(x) = x^2 - sin(x)+$, including the part $\verb+f(x) =+$.

1. The zero vector of the vector space $\mathbb{R}^{2}$ is .
   
   
2. The zero vector of the vector space of $2 \times 2$ matrices is .
   
   
3. The zero vector for the vector space of all functions $f : \mathbb{R} \to \mathbb{R}$ is .