Answer:
[tex]\begin{bmatrix}45 & 31 \\ 30 & 50\end{bmatrix}[/tex]
Step-by-step explanation:
Here, the given linear transformation ( from [tex]R^2[/tex] to [tex]R^2[/tex] ),
[tex]T(x) = B(A(x))[/tex]
[tex]T(x) = ( BA )( x)[/tex]
So when we consider the standard basis both sides, then matrix representation will be BA
That is, C = BA
Given,
[tex]A = \begin{bmatrix}1 & 9 \\ 8 & 6\end{bmatrix}[/tex]
[tex]B = \begin{bmatrix}0 & 4 \\ 5 & 3\end{bmatrix}[/tex]
[tex]\implies C = \begin{bmatrix}1 & 9 \\ 8 & 6\end{bmatrix}\begin{bmatrix}0 & 4 \\ 5 & 3\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}0+45 & 4+27 \\ 0+30 & 32+18\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}45 & 31 \\ 30 & 50\end{bmatrix}[/tex]
