# How to multiply a matrix by a vector

Using this example, could someone tell me how to multiply a matrix by a vector?

$$\left(\begin{array}{ccc} A & B & C \\ D & E & F \\ G & H & I \end{array}\right) * \left(\begin{array}{c} X \\ Y \\ Z \end{array} \right) = ?$$

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View the vector as a $3\times 1$ matrix; you know (I hope) how to multiply an $n\times p$ matrix by a $p\times m$ matrix to get an $n\times m$ matrix, right? Just do that. – Arturo Magidin Feb 21 '12 at 21:50
@Arturo There are people of all levels here, some of us are highly paid and highly intelligent, but didn't study math, so we don't know (and are trying to learn) how to multiply matrices. – Luke Puplett Mar 12 '13 at 17:48

$$\begin{pmatrix}AX+BY+CZ\\DX+EY+FZ\\GX+HY+IZ\end{pmatrix}$$