Matrix x Vector multiplication

• categories: Linear algebra, Definition

We can see it as vector wise, combination of all columns of $A$ ponderated by $x$

$$\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{33}& a_{33}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=x_1\left[\begin{array}{c}{a}_{11}\\ a_{21}\\ a_{31}\end{array}\right]+x_2\left[\begin{array}{c}{a}_{12}\\ a_{22}\\ a_{32}\end{array}\right]+x_3\left[\begin{array}{c}{a}_{13}\\ a_{23}\\ a_{33}\end{array}\right]$$