If $\left[\begin{array}{cc}{\lambda }^2-2\lambda +1& \lambda -2\\ 1-{\lambda }^2+3\lambda & 1-{\lambda }^2\end{array}\right]=A{\lambda }^2+B\lambda +C$  where A, B, C are matrices then B + C =

$put \lambda =1,$ we get A+B+C=$\left[\begin{array}{cc}0& -1\\ 3& 0\end{array}\right]$ , --------(1)  $put \lambda =-1 we get A-B+C=\left[\begin{array}{cc}4& -3\\ -3& 0\end{array}\right]$----------(2)

$put \lambda =0 we get C= \left[\begin{array}{cc}1& -2\\ 1& 1\end{array}\right]$

Eq (1)-(2)

2B=$\left[\begin{array}{cc}-4& 2\\ 6& 0\end{array}\right]$     $B=\left[\begin{array}{cc}-2& 1\\ 3& 0\end{array}\right]$

B+C=$\left[\begin{array}{cc}-1& -1\\ 4& 1\end{array}\right]$