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

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

$put \lambda =0$

$\Rightarrow C=\left[\begin{array}{r}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-2\\ 1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\end{array}\right]$

$\text{ Put }\lambda =1$

$\Rightarrow A+B+C=\left[\begin{array}{r}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-1\\ 3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\end{array}\right]----\left(1\right)$

$\text{ Put }\lambda =-1$

$\Rightarrow A-B+C=\left[\begin{array}{r}4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-3\\ -3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\end{array}\right]----\left(2\right)$

$\begin{array}{l}\Rightarrow B+C=\frac{(A+B+C)-(A-B+C)}{2}+C\\ =\left[\begin{array}{rr}-1& -1\\ 4& 1\end{array}\right]\end{array}$