- #1

evinda

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Let linear map $f: \mathbb{R}^3 \to \mathbb{R}^2$, $B$ basis (unknown) of $\mathbb{R}^3$ and $c=[(1,2),(3,4)]$ basis of $\mathbb{R}^2$. We are given the information that $cf_s=\begin{pmatrix}

1 & 0 & 1\\

2 & 1 & 0

\end{pmatrix}$. Let $v \in \mathbb{R}^3$, of which the coordinates as for $B$ are $(1,1,1)$. If $f(v)=(x_1, x_2)$, what does $x_2-x_1$ equal to?

I haven't really understood how we can find $x_1$ and $x_2$. Could you give me a hint? (Thinking)