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Let $S: \mathbb R^3 \rightarrow \mathbb R$

$v= (v_1,v_2,v_3) w= (w_1,w_2,w_3)$ Both w and v are vectors

Express the standard matrix $S: \mathbb R^3 \rightarrow \mathbb R$ in terms of $v_1,v_2,v_3$ and $w_1,w_2,w_3....$

I have trouble understanding the technique involved in deriving a standard matrix... What does $T(e_1), T(e_2)$, where $e1$ is $\langle 1,0,0\rangle$ and $e_2$ is $\langle 0,1,0\rangle$ have to do with it? (Note both $e_1$ and $e_2$ are vectors...)

Martin Argerami
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Chris Kim
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1 Answers1

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$T(e_1)$ is the image of $<1,0,0>$ under the map $T$. Once you compute this, you write it as a column in the matrix that describes the map . You do the same for $e_2$, $e_3$, etc., and this gives you the matrix that describes $T$ in the basis given by {$e_1, e_2, e_3$}

user99680
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