Let $$M = \left[\begin{array}{cc} -3 &3\cr -3 &1 \end{array}\right]$$ be a vector in the vector space $V$ of $2 \times 2$ matrices with real number entries. Let $$\mathcal{B} = \left\lbrace \left[\begin{array}{cc} 1 &0\cr 0 &0 \end{array}\right], \left[\begin{array}{cc} 0 &0\cr 0 &1 \end{array}\right], \left[\begin{array}{cc} 0 &0\cr 1 &0 \end{array}\right], \left[\begin{array}{cc} 0 &1\cr 0 &0 \end{array}\right] \right\rbrace$$ be an ordered basis for $V$.

1. Write $M$ as a linear combination of elements of $\mathcal{B}$.
   
   $\left[\begin{array}{cc} -3 &3\cr -3 &1 \end{array}\right] =$ $\left[\begin{array}{cc} 1 &0\cr 0 &0 \end{array}\right] +$ $\left[\begin{array}{cc} 0 &0\cr 0 &1 \end{array}\right] +$ $\left[\begin{array}{cc} 0 &0\cr 1 &0 \end{array}\right] +$ $\left[\begin{array}{cc} 0 &1\cr 0 &0 \end{array}\right].$
   
   
2. Let $\lbrack M \rbrack_{\mathcal{B}}$ denote the coordinate representation of $M$ relative to the basis $\mathcal{B}$. Find the coordinate vector representation for $M$ relative to the basis $\mathcal{B}$. Your answer should be a vector of the general form $\verb+<1,2,3,4>+$.
   
   $\lbrack M \rbrack_{\mathcal{B}} =$ .