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Just a short question regarding notation:

If this matrix represents a vector and I want to solve it for $t=2$, may I write it as follows:

$ \left( \begin{array}{ccc} vt\\ vt-gt\\ \end{array} \right)\{2\}=...$

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I've never seen that. The notation I've seen is this:

$\displaystyle \left.{\begin{pmatrix} vt \\ vt-gt \end{pmatrix}}\right\vert_{t = 2} = \begin{pmatrix} 2v \\ 2v-2g \end{pmatrix}$

The bar is read as "... evaluated at $t = 2$"

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