Matrix Product (Conventional)/Examples/3 x 3 Matrix-Vector

Example of (Conventional) Matrix Product

The $3 \times 3$ matrix-vector multiplication formula is an instance of the matrix product operation:

$\mathbf A \mathbf v = \begin{bmatrix}

a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \\ \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a_{11} x + a_{12} y + a_{13} z \\ a_{21} x + a_{22} y + a_{23} z \\ a_{31} x + a_{32} y + a_{33} z \\ \end{bmatrix}$

Sources

• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.2$: Functions on vectors: $\S 2.2.2$: $3 \times 3$ matrices