Define T: M 2,2 -> R by T
\[ Define T: M 2,2 -> R by T \begin{bmatrix} a & b \\ c & d \end{bmatrix} = a+b+c-d \]
Find the preimage of T-1 (3)
a + b + c - d = 3
\[ T-1 (3) = \begin{bmatrix} a & b \\ c & a+d+c-3 \end{bmatrix} \]
Examples of the possible subsets of pre-image:
\[ \begin{bmatrix} 1 & 2 \\ 3 & 3 \end{bmatrix} , \begin{bmatrix} 2 & 2 \\ 2 & 3 \end{bmatrix} , \begin{bmatrix} 0 & 0 \\ 0 & -3 \end{bmatrix} \]