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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 = [].

User OoOlly
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1 Answer

6 votes

Answer:


\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}

User TypingPanda
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