Question

Let A = [1 9 8 6] and b = [0 4 5 3]. Find the matrix C of the linear transformation T(x) = B(A(x)). C = [].

Answer 1

`\begin{bmatrix}45 & 31 \\ 30 & 50\end{bmatrix}`

Explanation:

Here, the given linear transformation ( from
`R^2` to
`R^2` ),

`T(x) = B(A(x))`

`T(x) = ( BA )( x)`

So when we consider the standard basis both sides, then matrix representation will be BA

That is, C = BA

Given,

`A = \begin{bmatrix}1 & 9 \\ 8 & 6\end{bmatrix}`

`B = \begin{bmatrix}0 & 4 \\ 5 & 3\end{bmatrix}`

`\implies C = \begin{bmatrix}1 & 9 \\ 8 & 6\end{bmatrix}\begin{bmatrix}0 & 4 \\ 5 & 3\end{bmatrix}`

`=\begin{bmatrix}0+45 & 4+27 \\ 0+30 & 32+18\end{bmatrix}`

`=\begin{bmatrix}45 & 31 \\ 30 & 50\end{bmatrix}`