- #1

evinda

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MHB

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Let $B=(b_1, b_2)$, $C=(c_1, c_2)$ basis of $\mathbb{R}^2$ and $L$ operator of $\mathbb{R}^2$, the matrix as for $B$ of which is $\begin{pmatrix}

2 & 2\\

1 & 0

\end{pmatrix}$. If $b_1=c_1+2c_2+b_2=c_1+3c_2$ and $A=\begin{pmatrix}

a_{11} & a_{12}\\

a_{21} & a_{22}

\end{pmatrix}$ the matrix of $L$ as for the basis $C$, what does the number $2a_{11}+3a_{12}+a_{21}+3a_{22}$ equal to? (Thinking)

In order to find the desired quantity, do we use the fact that the composition of C with $\begin{pmatrix}

2 & 2\\

1 & 0

\end{pmatrix}$ is equal to $A$ ? But how do we express the composition mathematically? We cannot multiply $C$ by the matrix, since the dimensions do not agree... (Worried)

Or am I somewhere wrong? (Thinking)